0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : run_vampire %s %d THM 0.10/0.31 % Computer : n009.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1920 0.10/0.31 % WCLimit : 240 0.10/0.31 % DateTime : Wed Jul 30 03:19:19 EDT 2025 0.10/0.31 % CPUTime : 0.16/0.33 This is a THF_ problem 0.16/0.33 Running higher-order theorem proving 0.18/0.37 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p -m 16384 -t 240 0.18/0.41 % (12309)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/183Mi) 0.18/0.41 % (12315)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/18Mi) 0.18/0.41 % (12312)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/2Mi) 0.18/0.41 % (12311)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/27Mi) 0.18/0.41 % (12313)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/2Mi) 0.18/0.41 % (12310)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/4Mi) 0.18/0.41 % (12314)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/275Mi) 0.18/0.41 % (12312)Instruction limit reached! 0.18/0.41 % (12312)------------------------------ 0.18/0.41 % (12312)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (12312)Termination reason: Unknown 0.18/0.41 % (12313)Instruction limit reached! 0.18/0.41 % (12313)------------------------------ 0.18/0.41 % (12313)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (12313)Termination reason: Unknown 0.18/0.41 % (12313)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (12313)Memory used [KB]: 1279 0.18/0.41 % (12313)Time elapsed: 0.004 s 0.18/0.41 % (12313)Instructions burned: 3 (million) 0.18/0.41 % (12313)------------------------------ 0.18/0.41 % (12313)------------------------------ 0.18/0.41 % (12312)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (12312)Memory used [KB]: 1279 0.18/0.41 % (12312)Time elapsed: 0.004 s 0.18/0.41 % (12312)Instructions burned: 3 (million) 0.18/0.41 % (12312)------------------------------ 0.18/0.41 % (12312)------------------------------ 0.18/0.41 % (12310)Instruction limit reached! 0.18/0.41 % (12310)------------------------------ 0.18/0.41 % (12310)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (12310)Termination reason: Unknown 0.18/0.41 % (12310)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (12310)Memory used [KB]: 1407 0.18/0.41 % (12310)Time elapsed: 0.005 s 0.18/0.41 % (12310)Instructions burned: 5 (million) 0.18/0.41 % (12310)------------------------------ 0.18/0.41 % (12310)------------------------------ 0.18/0.42 % (12315)Instruction limit reached! 0.18/0.42 % (12315)------------------------------ 0.18/0.42 % (12315)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.42 % (12315)Termination reason: Unknown 0.18/0.42 % (12315)Termination phase: Property scanning 0.18/0.42 0.18/0.42 % (12315)Memory used [KB]: 1535 0.18/0.42 % (12315)Time elapsed: 0.012 s 0.18/0.42 % (12315)Instructions burned: 19 (million) 0.18/0.42 % (12315)------------------------------ 0.18/0.42 % (12315)------------------------------ 0.22/0.42 % (12311)Instruction limit reached! 0.22/0.42 % (12311)------------------------------ 0.22/0.42 % (12311)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.42 % (12311)Termination reason: Unknown 0.22/0.42 % (12311)Termination phase: Property scanning 0.22/0.42 0.22/0.42 % (12311)Memory used [KB]: 1535 0.22/0.42 % (12311)Time elapsed: 0.016 s 0.22/0.42 % (12311)Instructions burned: 28 (million) 0.22/0.42 % (12311)------------------------------ 0.22/0.42 % (12311)------------------------------ 0.22/0.42 % (12317)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/37Mi) 0.22/0.42 % (12318)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/15Mi) 0.22/0.42 % (12316)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/3Mi) 0.22/0.42 % (12316)Instruction limit reached! 0.22/0.42 % (12316)------------------------------ 0.22/0.42 % (12316)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.42 % (12316)Termination reason: Unknown 0.22/0.42 % (12316)Termination phase: shuffling 0.22/0.42 0.22/0.42 % (12316)Memory used [KB]: 1279 0.22/0.42 % (12316)Time elapsed: 0.004 s 0.22/0.42 % (12316)Instructions burned: 4 (million) 0.22/0.42 % (12316)------------------------------ 0.22/0.42 % (12316)------------------------------ 0.22/0.43 % (12318)Instruction limit reached! 0.22/0.43 % (12318)------------------------------ 0.22/0.43 % (12318)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.43 % (12318)Termination reason: Unknown 0.22/0.43 % (12318)Termination phase: shuffling 0.22/0.43 0.22/0.43 % (12318)Memory used [KB]: 1407 0.22/0.43 % (12318)Time elapsed: 0.011 s 0.22/0.43 % (12318)Instructions burned: 17 (million) 0.22/0.43 % (12318)------------------------------ 0.22/0.43 % (12318)------------------------------ 0.22/0.43 % (12319)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/3Mi) 0.22/0.43 % (12319)Instruction limit reached! 0.22/0.43 % (12319)------------------------------ 0.22/0.43 % (12319)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.43 % (12319)Termination reason: Unknown 0.22/0.43 % (12319)Termination phase: shuffling 0.22/0.43 0.22/0.43 % (12319)Memory used [KB]: 1279 0.22/0.43 % (12319)Time elapsed: 0.004 s 0.22/0.43 % (12319)Instructions burned: 3 (million) 0.22/0.43 % (12319)------------------------------ 0.22/0.43 % (12319)------------------------------ 0.22/0.43 % (12320)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/1041Mi) 0.22/0.44 % (12317)Instruction limit reached! 0.22/0.44 % (12317)------------------------------ 0.22/0.44 % (12317)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.44 % (12317)Termination reason: Unknown 0.22/0.44 % (12317)Termination phase: Property scanning 0.22/0.44 0.22/0.44 % (12317)Memory used [KB]: 1791 0.22/0.44 % (12317)Time elapsed: 0.018 s 0.22/0.44 % (12317)Instructions burned: 37 (million) 0.22/0.44 % (12317)------------------------------ 0.22/0.44 % (12317)------------------------------ 0.22/0.44 % (12321)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/7Mi) 0.22/0.44 % (12321)Instruction limit reached! 0.22/0.44 % (12321)------------------------------ 0.22/0.44 % (12321)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.44 % (12321)Termination reason: Unknown 0.22/0.44 % (12321)Termination phase: shuffling 0.22/0.44 0.22/0.44 % (12321)Memory used [KB]: 1407 0.22/0.44 % (12321)Time elapsed: 0.006 s 0.22/0.44 % (12321)Instructions burned: 7 (million) 0.22/0.44 % (12321)------------------------------ 0.22/0.44 % (12321)------------------------------ 0.22/0.45 % (12322)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/16Mi) 0.22/0.45 % (12323)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/3Mi) 0.22/0.45 % (12323)Instruction limit reached! 0.22/0.45 % (12323)------------------------------ 0.22/0.45 % (12323)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.45 % (12323)Termination reason: Unknown 0.22/0.45 % (12323)Termination phase: shuffling 0.22/0.45 0.22/0.45 % (12323)Memory used [KB]: 1279 0.22/0.45 % (12323)Time elapsed: 0.003 s 0.22/0.45 % (12323)Instructions burned: 3 (million) 0.22/0.45 % (12323)------------------------------ 0.22/0.45 % (12323)------------------------------ 0.22/0.45 % (12324)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/3Mi) 0.22/0.45 % (12322)Instruction limit reached! 0.22/0.45 % (12322)------------------------------ 0.22/0.45 % (12322)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.45 % (12322)Termination reason: Unknown 0.22/0.45 % (12322)Termination phase: shuffling 0.22/0.45 0.22/0.45 % (12322)Memory used [KB]: 1407 0.22/0.45 % (12322)Time elapsed: 0.011 s 0.22/0.45 % (12322)Instructions burned: 17 (million) 0.22/0.45 % (12322)------------------------------ 0.22/0.45 % (12322)------------------------------ 0.22/0.45 % (12324)Instruction limit reached! 0.22/0.45 % (12324)------------------------------ 0.22/0.45 % (12324)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.45 % (12324)Termination reason: Unknown 0.22/0.45 % (12324)Termination phase: shuffling 0.22/0.45 0.22/0.45 % (12324)Memory used [KB]: 1279 0.22/0.45 % (12324)Time elapsed: 0.004 s 0.22/0.45 % (12324)Instructions burned: 4 (million) 0.22/0.45 % (12324)------------------------------ 0.22/0.45 % (12324)------------------------------ 0.22/0.46 % (12326)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/7Mi) 0.22/0.46 % (12326)Instruction limit reached! 0.22/0.46 % (12326)------------------------------ 0.22/0.46 % (12326)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.46 % (12326)Termination reason: Unknown 0.22/0.46 % (12326)Termination phase: shuffling 0.22/0.46 0.22/0.46 % (12326)Memory used [KB]: 1279 0.22/0.46 % (12326)Time elapsed: 0.006 s 0.22/0.46 % (12326)Instructions burned: 7 (million) 0.22/0.46 % (12326)------------------------------ 0.22/0.46 % (12326)------------------------------ 0.22/0.46 % (12327)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/3Mi) 0.22/0.46 % (12327)Instruction limit reached! 0.22/0.46 % (12327)------------------------------ 0.22/0.46 % (12327)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.46 % (12327)Termination reason: Unknown 0.22/0.46 % (12327)Termination phase: shuffling 0.22/0.46 0.22/0.46 % (12327)Memory used [KB]: 1279 0.22/0.46 % (12327)Time elapsed: 0.004 s 0.22/0.46 % (12327)Instructions burned: 3 (million) 0.22/0.46 % (12327)------------------------------ 0.22/0.46 % (12327)------------------------------ 0.22/0.47 % (12328)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/4Mi) 0.22/0.47 % (12329)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/18Mi) 0.22/0.47 % (12328)Instruction limit reached! 0.22/0.47 % (12328)------------------------------ 0.22/0.47 % (12328)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.47 % (12328)Termination reason: Unknown 0.22/0.47 % (12328)Termination phase: shuffling 0.22/0.47 0.22/0.47 % (12328)Memory used [KB]: 1279 0.22/0.47 % (12328)Time elapsed: 0.004 s 0.22/0.47 % (12328)Instructions burned: 4 (million) 0.22/0.47 % (12328)------------------------------ 0.22/0.47 % (12328)------------------------------ 0.22/0.47 % (12331)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/710Mi) 0.22/0.48 % (12329)Instruction limit reached! 0.22/0.48 % (12329)------------------------------ 0.22/0.48 % (12329)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.48 % (12329)Termination reason: Unknown 0.22/0.48 % (12329)Termination phase: Property scanning 0.22/0.48 0.22/0.48 % (12329)Memory used [KB]: 1535 0.22/0.48 % (12329)Time elapsed: 0.012 s 0.22/0.48 % (12329)Instructions burned: 19 (million) 0.22/0.48 % (12329)------------------------------ 0.22/0.48 % (12329)------------------------------ 0.22/0.48 % (12332)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_12196 for (2399ds/6Mi) 0.22/0.48 % (12332)Instruction limit reached! 0.22/0.48 % (12332)------------------------------ 0.22/0.48 % (12332)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.48 % (12332)Termination reason: Unknown 0.22/0.48 % (12332)Termination phase: shuffling 0.22/0.48 0.22/0.48 % (12332)Memory used [KB]: 1279 0.22/0.48 % (12332)Time elapsed: 0.006 s 0.22/0.48 % (12332)Instructions burned: 7 (million) 0.22/0.48 % (12332)------------------------------ 0.22/0.48 % (12332)------------------------------ 0.22/0.49 % (12333)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/902Mi) 0.22/0.49 % (12309)Instruction limit reached! 0.22/0.49 % (12309)------------------------------ 0.22/0.49 % (12309)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.49 % (12309)Termination reason: Unknown 0.22/0.49 % (12309)Termination phase: Saturation 0.22/0.49 0.22/0.49 % (12309)Memory used [KB]: 6652 0.22/0.49 % (12309)Time elapsed: 0.089 s 0.22/0.49 % (12309)Instructions burned: 184 (million) 0.22/0.49 % (12309)------------------------------ 0.22/0.49 % (12309)------------------------------ 0.22/0.49 % (12334)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/21Mi) 0.22/0.50 % (12335)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/5Mi) 0.22/0.50 % (12335)Instruction limit reached! 0.22/0.50 % (12335)------------------------------ 0.22/0.50 % (12335)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.50 % (12335)Termination reason: Unknown 0.22/0.50 % (12335)Termination phase: shuffling 0.22/0.50 0.22/0.50 % (12335)Memory used [KB]: 1407 0.22/0.50 % (12335)Time elapsed: 0.005 s 0.22/0.50 % (12335)Instructions burned: 6 (million) 0.22/0.50 % (12335)------------------------------ 0.22/0.50 % (12335)------------------------------ 0.22/0.50 % (12334)Instruction limit reached! 0.22/0.50 % (12334)------------------------------ 0.22/0.50 % (12334)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.50 % (12334)Termination reason: Unknown 0.22/0.50 % (12334)Termination phase: shuffling 0.22/0.50 0.22/0.50 % (12334)Memory used [KB]: 1407 0.22/0.50 % (12334)Time elapsed: 0.013 s 0.22/0.50 % (12334)Instructions burned: 21 (million) 0.22/0.50 % (12334)------------------------------ 0.22/0.50 % (12334)------------------------------ 0.22/0.51 % (12336)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/6Mi) 0.22/0.51 % (12336)Instruction limit reached! 0.22/0.51 % (12336)------------------------------ 0.22/0.51 % (12336)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.51 % (12336)Termination reason: Unknown 0.22/0.51 % (12336)Termination phase: shuffling 0.22/0.51 0.22/0.51 % (12336)Memory used [KB]: 1407 0.22/0.51 % (12336)Time elapsed: 0.005 s 0.22/0.51 % (12336)Instructions burned: 6 (million) 0.22/0.51 % (12336)------------------------------ 0.22/0.51 % (12336)------------------------------ 0.22/0.52 % (12337)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/377Mi) 0.22/0.52 % (12338)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/779Mi) 0.22/0.53 % (12339)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/19Mi) 0.22/0.53 % (12314)Instruction limit reached! 0.22/0.53 % (12314)------------------------------ 0.22/0.53 % (12314)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.53 % (12314)Termination reason: Unknown 0.22/0.53 % (12314)Termination phase: Saturation 0.22/0.53 0.22/0.53 % (12314)Memory used [KB]: 6652 0.22/0.53 % (12314)Time elapsed: 0.130 s 0.22/0.53 % (12314)Instructions burned: 276 (million) 0.22/0.53 % (12314)------------------------------ 0.22/0.53 % (12314)------------------------------ 0.22/0.53 % (12339)Instruction limit reached! 0.22/0.53 % (12339)------------------------------ 0.22/0.53 % (12339)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.53 % (12339)Termination reason: Unknown 0.22/0.53 % (12339)Termination phase: shuffling 0.22/0.53 0.22/0.53 % (12339)Memory used [KB]: 1663 0.22/0.53 % (12339)Time elapsed: 0.010 s 0.22/0.53 % (12339)Instructions burned: 19 (million) 0.22/0.53 % (12339)------------------------------ 0.22/0.53 % (12339)------------------------------ 0.22/0.54 % (12320)First to succeed. 0.22/0.55 % (12340)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/879Mi) 0.22/0.55 % (12341)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_12196 for (2398ds/17Mi) 0.22/0.55 % (12331)Also succeeded, but the first one will report. 0.22/0.55 % (12320)Refutation found. Thanks to Tanya! 0.22/0.55 % SZS status Theorem for E---3.1_12196 0.22/0.55 % SZS output start Proof for E---3.1_12196 0.22/0.55 thf(type_def_5, type, partia1833973666xt_a_b: $tType). 0.22/0.55 thf(type_def_6, type, a: $tType). 0.22/0.55 thf(type_def_7, type, set_a: $tType). 0.22/0.55 thf(type_def_9, type, int: $tType). 0.22/0.55 thf(type_def_10, type, product_prod_a_a: $tType). 0.22/0.55 thf(func_def_0, type, partia1833973666xt_a_b: $tType). 0.22/0.55 thf(func_def_1, type, product_prod_a_a: $tType). 0.22/0.55 thf(func_def_2, type, set_a: $tType). 0.22/0.55 thf(func_def_3, type, int: $tType). 0.22/0.55 thf(func_def_4, type, a: $tType). 0.22/0.55 thf(func_def_5, type, a_l_coset_a_b: partia1833973666xt_a_b > a > set_a > set_a). 0.22/0.55 thf(func_def_6, type, additi2104487374up_a_b: set_a > partia1833973666xt_a_b > $o). 0.22/0.55 thf(func_def_7, type, set_add_a_b: partia1833973666xt_a_b > set_a > set_a > set_a). 0.22/0.55 thf(func_def_8, type, partia1066395285xt_a_b: partia1833973666xt_a_b > set_a). 0.22/0.55 thf(func_def_9, type, mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a). 0.22/0.55 thf(func_def_10, type, minus_minus_int: int > int > int). 0.22/0.55 thf(func_def_11, type, minus_minus_set_a: set_a > set_a > set_a). 0.22/0.55 thf(func_def_12, type, plus_plus_int: int > int > int). 0.22/0.55 thf(func_def_13, type, uminus_uminus_int: int > int). 0.22/0.55 thf(func_def_14, type, uminus_uminus_set_a: set_a > set_a). 0.22/0.55 thf(func_def_15, type, locali1648887798ac_a_b: partia1833973666xt_a_b > set_a > $o). 0.22/0.55 thf(func_def_16, type, locali807230110ng_a_b: partia1833973666xt_a_b > set_a > $o). 0.22/0.55 thf(func_def_17, type, locali880295127ng_a_b: partia1833973666xt_a_b > set_a > $o). 0.22/0.55 thf(func_def_18, type, locali425460998xt_a_b: partia1833973666xt_a_b > set_a > $o). 0.22/0.55 thf(func_def_19, type, bot_bot_set_a: set_a). 0.22/0.55 thf(func_def_20, type, ord_less_eq_int: int > int > $o). 0.22/0.55 thf(func_def_21, type, ord_less_eq_set_a: set_a > set_a > $o). 0.22/0.55 thf(func_def_22, type, product_fst_a_a: product_prod_a_a > a). 0.22/0.55 thf(func_def_23, type, product_snd_a_a: product_prod_a_a > a). 0.22/0.55 thf(func_def_24, type, a_inv_a_b: partia1833973666xt_a_b > a > a). 0.22/0.55 thf(func_def_25, type, a_minus_a_b: partia1833973666xt_a_b > a > a > a). 0.22/0.55 thf(func_def_26, type, add_pow_a_b_int: partia1833973666xt_a_b > int > a > a). 0.22/0.55 thf(func_def_27, type, add_a_b: partia1833973666xt_a_b > a > a > a). 0.22/0.55 thf(func_def_28, type, zero_a_b: partia1833973666xt_a_b > a). 0.22/0.55 thf(func_def_29, type, semiring_a_b: partia1833973666xt_a_b > $o). 0.22/0.55 thf(func_def_30, type, collect_a: (a > $o) > set_a). 0.22/0.55 thf(func_def_31, type, member_a: a > set_a > $o). 0.22/0.55 thf(func_def_32, type, r: partia1833973666xt_a_b). 0.22/0.55 thf(func_def_33, type, s: set_a). 0.22/0.55 thf(func_def_34, type, r2: a). 0.22/0.55 thf(func_def_35, type, r3: a). 0.22/0.55 thf(func_def_36, type, s2: a). 0.22/0.55 thf(func_def_37, type, s3: a). 0.22/0.55 thf(func_def_38, type, t: a). 0.22/0.55 thf(func_def_39, type, t2: a). 0.22/0.55 thf(func_def_40, type, x: product_prod_a_a). 0.22/0.55 thf(func_def_41, type, y: product_prod_a_a). 0.22/0.55 thf(func_def_58, type, ph1: !>[X0: $tType]:(X0)). 0.22/0.55 thf(f1252,plain,( 0.22/0.55 $false), 0.22/0.55 inference(trivial_inequality_removal,[],[f1251])). 0.22/0.55 thf(f1251,plain,( 0.22/0.55 ($true = $false)), 0.22/0.55 inference(boolean_simplification,[],[f1250])). 0.22/0.55 thf(f1250,plain,( 0.22/0.55 ($true = (~ $true))), 0.22/0.55 inference(backward_demodulation,[],[f1130,f1249])). 0.22/0.55 thf(f1249,plain,( 0.22/0.55 ($true = ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (zero_a_b @ r))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))), 0.22/0.55 inference(boolean_simplification,[],[f1248])). 0.22/0.55 thf(f1248,plain,( 0.22/0.55 (($true => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (zero_a_b @ r))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))) = $true)), 0.22/0.55 inference(backward_demodulation,[],[f1145,f1242])). 0.22/0.55 thf(f1242,plain,( 0.22/0.55 ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) = $true)), 0.22/0.55 inference(boolean_simplification,[],[f1230])). 0.22/0.55 thf(f1230,plain,( 0.22/0.55 ($true = ($true => (member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r))))), 0.22/0.55 inference(superposition,[],[f1212,f871])). 0.22/0.55 thf(f871,plain,( 0.22/0.55 ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s) = $true)), 0.22/0.55 inference(cnf_transformation,[],[f339])). 0.22/0.55 thf(f339,plain,( 0.22/0.55 ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s) = $true)), 0.22/0.55 inference(fool_elimination,[],[f338])). 0.22/0.55 thf(f338,plain,( 0.22/0.55 (member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s)), 0.22/0.55 inference(rectify,[],[f45])). 0.22/0.55 thf(f45,axiom,( 0.22/0.55 (member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s)), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_65_f8)). 0.22/0.55 thf(f1212,plain,( 0.22/0.55 ( ! [X1 : a] : (($true = ((member_a @ X1 @ s) => (member_a @ X1 @ (partia1066395285xt_a_b @ r))))) )), 0.22/0.55 inference(beta_eta_normalization,[],[f1211])). 0.22/0.55 thf(f1211,plain,( 0.22/0.55 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((member_a @ Y0 @ s) => (member_a @ Y0 @ (partia1066395285xt_a_b @ r)))) @ X1))) )), 0.22/0.55 inference(pi_clausification,[],[f1054])). 0.22/0.55 thf(f1054,plain,( 0.22/0.55 ($true = (!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ s) => (member_a @ Y0 @ (partia1066395285xt_a_b @ r))))))), 0.22/0.55 inference(beta_eta_normalization,[],[f1028])). 0.22/0.55 thf(f1028,plain,( 0.22/0.55 (((^[Y0 : set_a]: ((^[Y1 : set_a]: (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y0) => (member_a @ Y2 @ Y1))))))) @ s @ (partia1066395285xt_a_b @ r)) = $true)), 0.22/0.55 inference(definition_unfolding,[],[f946,f709])). 0.22/0.55 thf(f709,plain,( 0.22/0.55 (ord_less_eq_set_a = (^[Y0 : set_a]: ((^[Y1 : set_a]: (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y0) => (member_a @ Y2 @ Y1))))))))), 0.22/0.55 inference(cnf_transformation,[],[f535])). 0.22/0.55 thf(f535,plain,( 0.22/0.55 (ord_less_eq_set_a = (^[Y0 : set_a]: ((^[Y1 : set_a]: (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y0) => (member_a @ Y2 @ Y1))))))))), 0.22/0.55 inference(fool_elimination,[],[f534])). 0.22/0.55 thf(f534,plain,( 0.22/0.55 (ord_less_eq_set_a = (^[X0 : set_a, X1 : set_a] : (! [X2 : a] : ((member_a @ X2 @ X0) => (member_a @ X2 @ X1)))))), 0.22/0.55 inference(rectify,[],[f204])). 0.22/0.55 thf(f204,axiom,( 0.22/0.55 (ord_less_eq_set_a = (^[X41 : set_a, X42 : set_a] : (! [X18 : a] : ((member_a @ X18 @ X41) => (member_a @ X18 @ X42)))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_243_subset__eq)). 0.22/0.55 thf(f946,plain,( 0.22/0.55 ((ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r)) = $true)), 0.22/0.55 inference(cnf_transformation,[],[f276])). 0.22/0.55 thf(f276,plain,( 0.22/0.55 ((ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r)) = $true)), 0.22/0.55 inference(fool_elimination,[],[f275])). 0.22/0.55 thf(f275,plain,( 0.22/0.55 (ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r))), 0.22/0.55 inference(rectify,[],[f65])). 0.22/0.55 thf(f65,axiom,( 0.22/0.55 (ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_142_subset)). 0.22/0.55 thf(f1145,plain,( 0.22/0.55 ($true = ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (zero_a_b @ r))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))), 0.22/0.55 inference(backward_demodulation,[],[f1135,f1144])). 0.22/0.55 thf(f1144,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (zero_a_b @ r))))), 0.22/0.55 inference(forward_demodulation,[],[f1143,f1101])). 0.22/0.55 thf(f1101,plain,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))), 0.22/0.55 inference(beta_eta_normalization,[],[f994])). 0.22/0.55 thf(f994,plain,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))), 0.22/0.55 inference(definition_unfolding,[],[f853,f865])). 0.22/0.55 thf(f865,plain,( 0.22/0.55 (a_minus_a_b = (^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))))), 0.22/0.55 inference(cnf_transformation,[],[f646])). 0.22/0.55 thf(f646,plain,( 0.22/0.55 (a_minus_a_b = (^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))))), 0.22/0.55 inference(fool_elimination,[],[f645])). 0.22/0.55 thf(f645,plain,( 0.22/0.55 (a_minus_a_b = (^[X0 : partia1833973666xt_a_b, X1 : a, X2 : a] : (add_a_b @ X0 @ X1 @ (a_inv_a_b @ X0 @ X2))))), 0.22/0.55 inference(rectify,[],[f165])). 0.22/0.55 thf(f165,axiom,( 0.22/0.55 (a_minus_a_b = (^[X37 : partia1833973666xt_a_b, X18 : a, X38 : a] : (add_a_b @ X37 @ X18 @ (a_inv_a_b @ X37 @ X38))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_130_a__minus__def)). 0.22/0.55 thf(f853,plain,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))), 0.22/0.55 inference(cnf_transformation,[],[f342])). 0.22/0.55 thf(f342,plain,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))), 0.22/0.55 inference(fool_elimination,[],[f90])). 0.22/0.55 thf(f90,axiom,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_58_f7)). 0.22/0.55 thf(f1143,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))))), 0.22/0.55 inference(forward_demodulation,[],[f1142,f1063])). 0.22/0.55 thf(f1063,plain,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t2 @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))))), 0.22/0.55 inference(beta_eta_normalization,[],[f989])). 0.22/0.55 thf(f989,plain,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t2 @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))), 0.22/0.55 inference(definition_unfolding,[],[f835,f865])). 0.22/0.55 thf(f835,plain,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))), 0.22/0.55 inference(cnf_transformation,[],[f680])). 0.22/0.55 thf(f680,plain,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))), 0.22/0.55 inference(fool_elimination,[],[f232])). 0.22/0.55 thf(f232,axiom,( 0.22/0.55 ((zero_a_b @ r) = (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_57_f5)). 0.22/0.55 thf(f1142,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))))), 0.22/0.55 inference(forward_demodulation,[],[f1052,f1128])). 0.22/0.55 thf(f1128,plain,( 0.22/0.55 ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)))), 0.22/0.55 inference(backward_demodulation,[],[f1118,f1063])). 0.22/0.55 thf(f1118,plain,( 0.22/0.55 ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))))), 0.22/0.55 inference(backward_demodulation,[],[f1104,f1098])). 0.22/0.55 thf(f1098,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))))), 0.22/0.55 inference(beta_eta_normalization,[],[f1008])). 0.22/0.55 thf(f1008,plain,( 0.22/0.55 ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) = ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))), 0.22/0.55 inference(definition_unfolding,[],[f892,f865,f865])). 0.22/0.55 thf(f892,plain,( 0.22/0.55 ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))), 0.22/0.55 inference(cnf_transformation,[],[f618])). 0.22/0.55 thf(f618,plain,( 0.22/0.55 ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))), 0.22/0.55 inference(fool_elimination,[],[f42])). 0.22/0.55 thf(f42,axiom,( 0.22/0.55 ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) = (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_41_f25)). 0.22/0.55 thf(f1104,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))))), 0.22/0.55 inference(beta_eta_normalization,[],[f1016])). 0.22/0.55 thf(f1016,plain,( 0.22/0.55 ((mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) = ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))), 0.22/0.55 inference(definition_unfolding,[],[f920,f865,f865])). 0.22/0.55 thf(f920,plain,( 0.22/0.55 ((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))), 0.22/0.55 inference(cnf_transformation,[],[f663])). 0.22/0.55 thf(f663,plain,( 0.22/0.55 ((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))), 0.22/0.55 inference(fool_elimination,[],[f115])). 0.22/0.55 thf(f115,axiom,( 0.22/0.55 ((a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_42_f32)). 0.22/0.55 thf(f1052,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))), 0.22/0.55 inference(beta_eta_normalization,[],[f992])). 0.22/0.55 thf(f992,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))), 0.22/0.55 inference(definition_unfolding,[],[f850,f865,f865,f865,f865])). 0.22/0.55 thf(f850,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))), 0.22/0.55 inference(cnf_transformation,[],[f473])). 0.22/0.55 thf(f473,plain,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))), 0.22/0.55 inference(fool_elimination,[],[f23])). 0.22/0.55 thf(f23,axiom,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_19_f40)). 0.22/0.55 thf(f1135,plain,( 0.22/0.55 ($true = ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))), 0.22/0.55 inference(forward_demodulation,[],[f1134,f1128])). 0.22/0.55 thf(f1134,plain,( 0.22/0.55 ($true = ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))), 0.22/0.55 inference(boolean_simplification,[],[f1133])). 0.22/0.55 thf(f1133,plain,( 0.22/0.55 ($true = ($true => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))))), 0.22/0.55 inference(forward_demodulation,[],[f1132,f1082])). 0.22/0.55 thf(f1082,plain,( 0.22/0.55 ($true = (member_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)))), 0.22/0.55 inference(beta_eta_normalization,[],[f1014])). 0.22/0.55 thf(f1014,plain,( 0.22/0.55 ($true = (member_a @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)))), 0.22/0.55 inference(definition_unfolding,[],[f915,f865])). 0.22/0.55 thf(f915,plain,( 0.22/0.55 ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) = $true)), 0.22/0.55 inference(cnf_transformation,[],[f652])). 0.22/0.55 thf(f652,plain,( 0.22/0.55 ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) = $true)), 0.22/0.55 inference(fool_elimination,[],[f651])). 0.22/0.55 thf(f651,plain,( 0.22/0.55 (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r))), 0.22/0.55 inference(rectify,[],[f109])). 0.22/0.55 thf(f109,axiom,( 0.22/0.55 (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_13_f42)). 0.22/0.55 thf(f1132,plain,( 0.22/0.55 ($true = ((member_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))))), 0.22/0.55 inference(boolean_simplification,[],[f1131])). 0.22/0.55 thf(f1131,plain,( 0.22/0.55 ($true = ($true => ((member_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))))), 0.22/0.55 inference(forward_demodulation,[],[f1062,f1107])). 0.22/0.55 thf(f1107,plain,( 0.22/0.55 ($true = (member_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)))), 0.22/0.55 inference(beta_eta_normalization,[],[f980])). 0.22/0.55 thf(f980,plain,( 0.22/0.55 ($true = (member_a @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)))), 0.22/0.55 inference(definition_unfolding,[],[f807,f865])). 0.22/0.55 thf(f807,plain,( 0.22/0.55 ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)) = $true)), 0.22/0.55 inference(cnf_transformation,[],[f402])). 0.22/0.55 thf(f402,plain,( 0.22/0.55 ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)) = $true)), 0.22/0.55 inference(fool_elimination,[],[f401])). 0.22/0.55 thf(f401,plain,( 0.22/0.55 (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r))), 0.22/0.55 inference(rectify,[],[f81])). 0.22/0.55 thf(f81,axiom,( 0.22/0.55 (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_12_f41)). 0.22/0.55 thf(f1062,plain,( 0.22/0.55 ($true = ((member_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))))), 0.22/0.55 inference(beta_eta_normalization,[],[f985])). 0.22/0.55 thf(f985,plain,( 0.22/0.55 (((member_a @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))) = $true)), 0.22/0.55 inference(definition_unfolding,[],[f823,f865,f865,f865,f865,f865,f865])). 0.22/0.55 thf(f823,plain,( 0.22/0.55 ($true = ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))))), 0.22/0.55 inference(cnf_transformation,[],[f281])). 0.22/0.55 thf(f281,plain,( 0.22/0.55 ($true = ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))))), 0.22/0.55 inference(fool_elimination,[],[f280])). 0.22/0.55 thf(f280,plain,( 0.22/0.55 (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))), 0.22/0.55 inference(rectify,[],[f221])). 0.22/0.55 thf(f221,axiom,( 0.22/0.55 (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r)) => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062)). 0.22/0.55 thf(f1130,plain,( 0.22/0.55 ($true = (~ ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (zero_a_b @ r))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))), 0.22/0.55 inference(backward_demodulation,[],[f1115,f1063])). 0.22/0.55 thf(f1115,plain,( 0.22/0.55 ($true = (~ ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (zero_a_b @ r))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))), 0.22/0.55 inference(backward_demodulation,[],[f1109,f1101])). 0.22/0.55 thf(f1109,plain,( 0.22/0.55 ($true = (~ ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x)))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))), 0.22/0.55 inference(beta_eta_normalization,[],[f1024])). 0.22/0.55 thf(f1024,plain,( 0.22/0.55 ($true = (~ ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ ((^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))) @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))), 0.22/0.55 inference(definition_unfolding,[],[f937,f865,f865,f865,f865])). 0.22/0.55 thf(f937,plain,( 0.22/0.55 ($true = (~ ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))), 0.22/0.55 inference(cnf_transformation,[],[f583])). 0.22/0.55 thf(f583,plain,( 0.22/0.55 ($true = (~ ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))), 0.22/0.55 inference(fool_elimination,[],[f141])). 0.22/0.55 thf(f141,negated_conjecture,( 0.22/0.55 ~((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))), 0.22/0.55 inference(negated_conjecture,[],[f140])). 0.22/0.55 thf(f140,conjecture,( 0.22/0.55 ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ t2 @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ r2) @ (mult_a_ring_ext_a_b @ r @ s2 @ (product_fst_a_a @ x))))) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y)))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))), 0.22/0.55 file('/export/starexec/sandbox2/tmp/tmp.KAMFn1X2mc/E---3.1_12196.p',conj_0)). 0.22/0.55 % SZS output end Proof for E---3.1_12196 0.22/0.55 % (12320)------------------------------ 0.22/0.55 % (12320)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.55 % (12320)Termination reason: Refutation 0.22/0.55 0.22/0.55 % (12320)Memory used [KB]: 7547 0.22/0.55 % (12320)Time elapsed: 0.120 s 0.22/0.55 % (12320)Instructions burned: 238 (million) 0.22/0.55 % (12320)------------------------------ 0.22/0.55 % (12320)------------------------------ 0.22/0.55 % (12308)Success in time 0.181 s 0.22/0.56 EOF