0.05/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s 0.11/0.32 % Computer : n010.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 300 0.11/0.32 % WCLimit : 300 0.11/0.32 % DateTime : Fri Jul 5 04:28:24 EDT 2024 0.11/0.32 % CPUTime : 0.11/0.34 This is a THF_ problem 0.11/0.34 Running vampire_ho --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.37 % (15323)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi) 0.11/0.37 % (15320)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on theBenchmark for (2999ds/36Mi) 0.11/0.37 % (15324)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on theBenchmark for (2999ds/74Mi) 0.11/0.37 % (15322)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on theBenchmark for (2999ds/385Mi) 0.11/0.37 % (15325)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi) 0.11/0.37 % (15326)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on theBenchmark for (2999ds/915Mi) 0.11/0.37 % (15321)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on theBenchmark for (2999ds/34Mi) 0.11/0.37 % (15319)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2999ds/96Mi) 0.11/0.37 % (15325)Instruction limit reached! 0.11/0.37 % (15325)------------------------------ 0.11/0.37 % (15325)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.11/0.37 % (15325)Termination reason: Unknown 0.11/0.37 % (15325)Termination phase: shuffling 0.11/0.37 0.11/0.37 % (15325)Memory used [KB]: 1279 0.11/0.37 % (15325)Time elapsed: 0.004 s 0.11/0.37 % (15325)Instructions burned: 5 (million) 0.11/0.37 % (15325)------------------------------ 0.11/0.37 % (15325)------------------------------ 0.11/0.38 % (15323)Instruction limit reached! 0.11/0.38 % (15323)------------------------------ 0.11/0.38 % (15323)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.11/0.38 % (15323)Termination reason: Unknown 0.11/0.38 % (15323)Termination phase: shuffling 0.11/0.38 0.11/0.38 % (15323)Memory used [KB]: 1535 0.11/0.38 % (15323)Time elapsed: 0.010 s 0.11/0.38 % (15323)Instructions burned: 18 (million) 0.11/0.38 % (15323)------------------------------ 0.11/0.38 % (15323)------------------------------ 0.11/0.38 % (15320)Instruction limit reached! 0.11/0.38 % (15320)------------------------------ 0.11/0.38 % (15320)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.11/0.38 % (15320)Termination reason: Unknown 0.11/0.38 % (15320)Termination phase: Preprocessing 3 0.11/0.38 0.11/0.38 % (15320)Memory used [KB]: 1663 0.11/0.38 % (15320)Time elapsed: 0.017 s 0.11/0.38 % (15320)Instructions burned: 36 (million) 0.11/0.38 % (15320)------------------------------ 0.11/0.38 % (15320)------------------------------ 0.11/0.39 % (15327)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 theBenchmark for (2999ds/21Mi) 0.11/0.39 % (15321)Instruction limit reached! 0.11/0.39 % (15321)------------------------------ 0.11/0.39 % (15321)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.11/0.39 % (15321)Termination reason: Unknown 0.11/0.39 % (15321)Termination phase: shuffling 0.11/0.39 0.11/0.39 % (15321)Memory used [KB]: 1663 0.11/0.39 % (15321)Time elapsed: 0.017 s 0.11/0.39 % (15321)Instructions burned: 35 (million) 0.11/0.39 % (15321)------------------------------ 0.11/0.39 % (15321)------------------------------ 0.18/0.39 % (15328)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi) 0.18/0.40 % (15327)Instruction limit reached! 0.18/0.40 % (15327)------------------------------ 0.18/0.40 % (15327)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.40 % (15327)Termination reason: Unknown 0.18/0.40 % (15327)Termination phase: shuffling 0.18/0.40 0.18/0.40 % (15327)Memory used [KB]: 1535 0.18/0.40 % (15327)Time elapsed: 0.011 s 0.18/0.40 % (15327)Instructions burned: 21 (million) 0.18/0.40 % (15327)------------------------------ 0.18/0.40 % (15327)------------------------------ 0.18/0.40 % (15328)Instruction limit reached! 0.18/0.40 % (15328)------------------------------ 0.18/0.40 % (15328)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.40 % (15328)Termination reason: Unknown 0.18/0.40 % (15328)Termination phase: shuffling 0.18/0.40 0.18/0.40 % (15328)Memory used [KB]: 1407 0.18/0.40 % (15328)Time elapsed: 0.005 s 0.18/0.40 % (15328)Instructions burned: 7 (million) 0.18/0.40 % (15328)------------------------------ 0.18/0.40 % (15328)------------------------------ 0.18/0.40 % (15329)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on theBenchmark for (2999ds/1021Mi) 0.18/0.40 % (15324)Instruction limit reached! 0.18/0.40 % (15324)------------------------------ 0.18/0.40 % (15324)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.40 % (15324)Termination reason: Unknown 0.18/0.40 % (15324)Termination phase: Function definition elimination 0.18/0.40 0.18/0.40 % (15324)Memory used [KB]: 1918 0.18/0.40 % (15324)Time elapsed: 0.030 s 0.18/0.40 % (15324)Instructions burned: 76 (million) 0.18/0.40 % (15324)------------------------------ 0.18/0.40 % (15324)------------------------------ 0.18/0.40 % (15330)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2999ds/71Mi) 0.18/0.40 % (15326)Refutation not found, incomplete strategy 0.18/0.40 % (15326)------------------------------ 0.18/0.40 % (15326)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.40 % (15326)Termination reason: Refutation not found, incomplete strategy 0.18/0.40 0.18/0.40 0.18/0.40 % (15326)Memory used [KB]: 6396 0.18/0.40 % (15326)Time elapsed: 0.036 s 0.18/0.40 % (15326)Instructions burned: 76 (million) 0.18/0.40 % (15326)------------------------------ 0.18/0.40 % (15326)------------------------------ 0.18/0.41 % (15332)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on theBenchmark for (2999ds/1044Mi) 0.18/0.41 % (15331)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=9:si=on:rtra=on_0 on theBenchmark for (2999ds/9Mi) 0.18/0.41 % (15319)Instruction limit reached! 0.18/0.41 % (15319)------------------------------ 0.18/0.41 % (15319)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.41 % (15319)Termination reason: Unknown 0.18/0.41 % (15319)Termination phase: Function definition elimination 0.18/0.41 0.18/0.41 % (15319)Memory used [KB]: 1791 0.18/0.41 % (15319)Time elapsed: 0.041 s 0.18/0.41 % (15319)Instructions burned: 97 (million) 0.18/0.41 % (15319)------------------------------ 0.18/0.41 % (15319)------------------------------ 0.18/0.41 % (15331)Instruction limit reached! 0.18/0.41 % (15331)------------------------------ 0.18/0.41 % (15331)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.41 % (15331)Termination reason: Unknown 0.18/0.41 % (15331)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (15331)Memory used [KB]: 1407 0.18/0.41 % (15331)Time elapsed: 0.006 s 0.18/0.41 % (15331)Instructions burned: 11 (million) 0.18/0.41 % (15331)------------------------------ 0.18/0.41 % (15331)------------------------------ 0.18/0.42 % (15334)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on theBenchmark for (2999ds/61Mi) 0.18/0.42 % (15335)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on theBenchmark for (2999ds/14Mi) 0.18/0.42 % (15333)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on theBenchmark for (2999ds/128Mi) 0.18/0.43 % (15330)Instruction limit reached! 0.18/0.43 % (15330)------------------------------ 0.18/0.43 % (15330)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.43 % (15330)Termination reason: Unknown 0.18/0.43 % (15330)Termination phase: Function definition elimination 0.18/0.43 0.18/0.43 % (15330)Memory used [KB]: 1791 0.18/0.43 % (15330)Time elapsed: 0.030 s 0.18/0.43 % (15330)Instructions burned: 73 (million) 0.18/0.43 % (15330)------------------------------ 0.18/0.43 % (15330)------------------------------ 0.18/0.43 % (15335)Instruction limit reached! 0.18/0.43 % (15335)------------------------------ 0.18/0.43 % (15335)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.43 % (15335)Termination reason: Unknown 0.18/0.43 % (15335)Termination phase: shuffling 0.18/0.43 0.18/0.43 % (15335)Memory used [KB]: 1535 0.18/0.43 % (15335)Time elapsed: 0.007 s 0.18/0.43 % (15335)Instructions burned: 16 (million) 0.18/0.43 % (15335)------------------------------ 0.18/0.43 % (15335)------------------------------ 0.18/0.43 % (15336)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi) 0.18/0.43 % (15336)Instruction limit reached! 0.18/0.43 % (15336)------------------------------ 0.18/0.43 % (15336)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.43 % (15336)Termination reason: Unknown 0.18/0.43 % (15336)Termination phase: shuffling 0.18/0.43 0.18/0.43 % (15336)Memory used [KB]: 1279 0.18/0.43 % (15336)Time elapsed: 0.003 s 0.18/0.43 % (15336)Instructions burned: 2 (million) 0.18/0.43 % (15336)------------------------------ 0.18/0.43 % (15336)------------------------------ 0.18/0.44 % (15337)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 theBenchmark for (2999ds/1041Mi) 0.18/0.44 % (15338)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2999ds/11Mi) 0.18/0.44 % (15334)Instruction limit reached! 0.18/0.44 % (15334)------------------------------ 0.18/0.44 % (15334)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.44 % (15334)Termination reason: Unknown 0.18/0.44 % (15334)Termination phase: Function definition elimination 0.18/0.44 0.18/0.44 % (15334)Memory used [KB]: 1791 0.18/0.44 % (15334)Time elapsed: 0.027 s 0.18/0.44 % (15334)Instructions burned: 62 (million) 0.18/0.44 % (15334)------------------------------ 0.18/0.44 % (15334)------------------------------ 0.18/0.45 % (15338)Instruction limit reached! 0.18/0.45 % (15338)------------------------------ 0.18/0.45 % (15338)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.45 % (15338)Termination reason: Unknown 0.18/0.45 % (15338)Termination phase: shuffling 0.18/0.45 0.18/0.45 % (15338)Memory used [KB]: 1535 0.18/0.45 % (15338)Time elapsed: 0.007 s 0.18/0.45 % (15338)Instructions burned: 12 (million) 0.18/0.45 % (15338)------------------------------ 0.18/0.45 % (15338)------------------------------ 0.18/0.45 % (15339)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2999ds/140Mi) 0.18/0.46 % (15341)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on theBenchmark for (2999ds/56Mi) 0.18/0.46 % (15340)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2999ds/26Mi) 0.18/0.47 % (15333)Instruction limit reached! 0.18/0.47 % (15333)------------------------------ 0.18/0.47 % (15333)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.47 % (15333)Termination reason: Unknown 0.18/0.47 % (15333)Termination phase: Function definition elimination 0.18/0.47 0.18/0.47 % (15333)Memory used [KB]: 1791 0.18/0.47 % (15333)Time elapsed: 0.044 s 0.18/0.47 % (15333)Instructions burned: 129 (million) 0.18/0.47 % (15333)------------------------------ 0.18/0.47 % (15333)------------------------------ 0.18/0.47 % (15339)Refutation not found, incomplete strategy 0.18/0.47 % (15339)------------------------------ 0.18/0.47 % (15339)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.47 % (15339)Termination reason: Refutation not found, incomplete strategy 0.18/0.47 0.18/0.47 0.18/0.47 % (15339)Memory used [KB]: 6140 0.18/0.47 % (15339)Time elapsed: 0.051 s 0.18/0.47 % (15339)Instructions burned: 50 (million) 0.18/0.47 % (15339)------------------------------ 0.18/0.47 % (15339)------------------------------ 0.18/0.47 % (15340)Instruction limit reached! 0.18/0.47 % (15340)------------------------------ 0.18/0.47 % (15340)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.47 % (15340)Termination reason: Unknown 0.18/0.47 % (15340)Termination phase: Property scanning 0.18/0.47 0.18/0.47 % (15340)Memory used [KB]: 1663 0.18/0.47 % (15340)Time elapsed: 0.013 s 0.18/0.47 % (15340)Instructions burned: 26 (million) 0.18/0.47 % (15340)------------------------------ 0.18/0.47 % (15340)------------------------------ 0.18/0.48 % (15342)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2998ds/275Mi) 0.18/0.48 % (15341)Instruction limit reached! 0.18/0.48 % (15341)------------------------------ 0.18/0.48 % (15341)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.48 % (15341)Termination reason: Unknown 0.18/0.48 % (15341)Termination phase: Function definition elimination 0.18/0.48 0.18/0.48 % (15341)Memory used [KB]: 1791 0.18/0.48 % (15341)Time elapsed: 0.026 s 0.18/0.48 % (15341)Instructions burned: 60 (million) 0.18/0.48 % (15341)------------------------------ 0.18/0.48 % (15341)------------------------------ 0.18/0.48 % (15343)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi) 0.18/0.49 % (15343)Instruction limit reached! 0.18/0.49 % (15343)------------------------------ 0.18/0.49 % (15343)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.49 % (15322)Instruction limit reached! 0.18/0.49 % (15322)------------------------------ 0.18/0.49 % (15322)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.49 % (15322)Termination reason: Unknown 0.18/0.49 % (15322)Termination phase: Property scanning 0.18/0.49 0.18/0.49 % (15322)Memory used [KB]: 1918 0.18/0.49 % (15322)Time elapsed: 0.118 s 0.18/0.49 % (15322)Instructions burned: 386 (million) 0.18/0.49 % (15322)------------------------------ 0.18/0.49 % (15322)------------------------------ 0.18/0.49 % (15343)Termination reason: Unknown 0.18/0.49 % (15343)Termination phase: shuffling 0.18/0.49 0.18/0.49 % (15343)Memory used [KB]: 1279 0.18/0.49 % (15343)Time elapsed: 0.003 s 0.18/0.49 % (15343)Instructions burned: 3 (million) 0.18/0.49 % (15343)------------------------------ 0.18/0.49 % (15343)------------------------------ 0.18/0.49 % (15344)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 theBenchmark for (2998ds/19Mi) 0.18/0.49 % (15332)First to succeed. 0.18/0.50 % (15332)Refutation found. Thanks to Tanya! 0.18/0.50 % SZS status Theorem for theBenchmark 0.18/0.50 % SZS output start Proof for theBenchmark 0.18/0.50 thf(func_def_0, type, is_of: $i > ($i > $o) > $o). 0.18/0.50 thf(func_def_2, type, all_of: ($i > $o) > ($i > $o) > $o). 0.18/0.50 thf(func_def_3, type, eps: ($i > $o) > $i). 0.18/0.50 thf(func_def_4, type, in: $i > $i > $o). 0.18/0.50 thf(func_def_5, type, d_Subq: $i > $i > $o). 0.18/0.50 thf(func_def_7, type, union: $i > $i). 0.18/0.50 thf(func_def_8, type, power: $i > $i). 0.18/0.50 thf(func_def_9, type, repl: $i > ($i > $i) > $i). 0.18/0.50 thf(func_def_10, type, d_Union_closed: $i > $o). 0.18/0.50 thf(func_def_11, type, d_Power_closed: $i > $o). 0.18/0.50 thf(func_def_12, type, d_Repl_closed: $i > $o). 0.18/0.50 thf(func_def_13, type, d_ZF_closed: $i > $o). 0.18/0.50 thf(func_def_14, type, univof: $i > $i). 0.18/0.50 thf(func_def_15, type, if: $o > $i > $i > $i). 0.18/0.50 thf(func_def_16, type, nIn: $i > $i > $o). 0.18/0.50 thf(func_def_17, type, d_UPair: $i > $i > $i). 0.18/0.50 thf(func_def_18, type, d_Sing: $i > $i). 0.18/0.50 thf(func_def_19, type, binunion: $i > $i > $i). 0.18/0.50 thf(func_def_20, type, famunion: $i > ($i > $i) > $i). 0.18/0.50 thf(func_def_21, type, d_Sep: $i > ($i > $o) > $i). 0.18/0.50 thf(func_def_22, type, d_ReplSep: $i > ($i > $o) > ($i > $i) > $i). 0.18/0.50 thf(func_def_23, type, setminus: $i > $i > $i). 0.18/0.50 thf(func_def_24, type, d_In_rec_G: ($i > ($i > $i) > $i) > $i > $i > $o). 0.18/0.50 thf(func_def_25, type, d_In_rec: ($i > ($i > $i) > $i) > $i > $i). 0.18/0.50 thf(func_def_26, type, ordsucc: $i > $i). 0.18/0.50 thf(func_def_27, type, nat_p: $i > $o). 0.18/0.50 thf(func_def_29, type, d_Inj1: $i > $i). 0.18/0.50 thf(func_def_30, type, d_Inj0: $i > $i). 0.18/0.50 thf(func_def_31, type, d_Unj: $i > $i). 0.18/0.50 thf(func_def_32, type, pair: $i > $i > $i). 0.18/0.50 thf(func_def_33, type, proj0: $i > $i). 0.18/0.50 thf(func_def_34, type, proj1: $i > $i). 0.18/0.50 thf(func_def_35, type, d_Sigma: $i > ($i > $i) > $i). 0.18/0.50 thf(func_def_36, type, setprod: $i > $i > $i). 0.18/0.50 thf(func_def_37, type, ap: $i > $i > $i). 0.18/0.50 thf(func_def_38, type, pair_p: $i > $o). 0.18/0.50 thf(func_def_39, type, d_Pi: $i > ($i > $i) > $i). 0.18/0.50 thf(func_def_40, type, imp: $o > $o > $o). 0.18/0.50 thf(func_def_41, type, d_not: $o > $o). 0.18/0.50 thf(func_def_42, type, wel: $o > $o). 0.18/0.50 thf(func_def_44, type, l_ec: $o > $o > $o). 0.18/0.50 thf(func_def_45, type, d_and: $o > $o > $o). 0.18/0.50 thf(func_def_46, type, l_or: $o > $o > $o). 0.18/0.50 thf(func_def_47, type, orec: $o > $o > $o). 0.18/0.50 thf(func_def_48, type, l_iff: $o > $o > $o). 0.18/0.50 thf(func_def_49, type, all: $i > ($i > $o) > $o). 0.18/0.50 thf(func_def_50, type, non: $i > ($i > $o) > $i > $o). 0.18/0.50 thf(func_def_51, type, l_some: $i > ($i > $o) > $o). 0.18/0.50 thf(func_def_52, type, or3: $o > $o > $o > $o). 0.18/0.50 thf(func_def_53, type, and3: $o > $o > $o > $o). 0.18/0.50 thf(func_def_54, type, ec3: $o > $o > $o > $o). 0.18/0.50 thf(func_def_55, type, orec3: $o > $o > $o > $o). 0.18/0.50 thf(func_def_56, type, e_is: $i > $i > $i > $o). 0.18/0.50 thf(func_def_57, type, amone: $i > ($i > $o) > $o). 0.18/0.50 thf(func_def_58, type, one: $i > ($i > $o) > $o). 0.18/0.50 thf(func_def_59, type, ind: $i > ($i > $o) > $i). 0.18/0.50 thf(func_def_60, type, injective: $i > $i > $i > $o). 0.18/0.50 thf(func_def_61, type, image: $i > $i > $i > $i > $o). 0.18/0.50 thf(func_def_62, type, tofs: $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_63, type, soft: $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_64, type, inverse: $i > $i > $i > $i). 0.18/0.50 thf(func_def_65, type, surjective: $i > $i > $i > $o). 0.18/0.50 thf(func_def_66, type, bijective: $i > $i > $i > $o). 0.18/0.50 thf(func_def_67, type, invf: $i > $i > $i > $i). 0.18/0.50 thf(func_def_68, type, inj_h: $i > $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_69, type, e_in: $i > ($i > $o) > $i > $i). 0.18/0.50 thf(func_def_70, type, out: $i > ($i > $o) > $i > $i). 0.18/0.50 thf(func_def_71, type, d_pair: $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_72, type, first: $i > $i > $i > $i). 0.18/0.50 thf(func_def_73, type, second: $i > $i > $i > $i). 0.18/0.50 thf(func_def_74, type, prop1: $o > $i > $i > $i > $i > $o). 0.18/0.50 thf(func_def_75, type, ite: $o > $i > $i > $i > $i). 0.18/0.50 thf(func_def_76, type, wissel_wa: $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_77, type, wissel_wb: $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_78, type, wissel: $i > $i > $i > $i). 0.18/0.50 thf(func_def_79, type, changef: $i > $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_80, type, r_ec: $o > $o > $o). 0.18/0.50 thf(func_def_81, type, esti: $i > $i > $i > $o). 0.18/0.50 thf(func_def_82, type, empty: $i > $i > $o). 0.18/0.50 thf(func_def_83, type, nonempty: $i > $i > $o). 0.18/0.50 thf(func_def_84, type, incl: $i > $i > $i > $o). 0.18/0.50 thf(func_def_85, type, st_disj: $i > $i > $i > $o). 0.18/0.50 thf(func_def_86, type, nissetprop: $i > $i > $i > $i > $o). 0.18/0.50 thf(func_def_87, type, unmore: $i > $i > $i > $i). 0.18/0.50 thf(func_def_88, type, ecelt: $i > ($i > $i > $o) > $i > $i). 0.18/0.50 thf(func_def_89, type, ecp: $i > ($i > $i > $o) > $i > $i > $o). 0.18/0.50 thf(func_def_90, type, anec: $i > ($i > $i > $o) > $i > $o). 0.18/0.50 thf(func_def_91, type, ect: $i > ($i > $i > $o) > $i). 0.18/0.50 thf(func_def_92, type, ectset: $i > ($i > $i > $o) > $i > $i). 0.18/0.50 thf(func_def_93, type, ectelt: $i > ($i > $i > $o) > $i > $i). 0.18/0.50 thf(func_def_94, type, ecect: $i > ($i > $i > $o) > $i > $i). 0.18/0.50 thf(func_def_95, type, fixfu: $i > ($i > $i > $o) > $i > $i > $o). 0.18/0.50 thf(func_def_96, type, d_10_prop1: $i > ($i > $i > $o) > $i > $i > $i > $i > $i > $o). 0.18/0.50 thf(func_def_97, type, prop2: $i > ($i > $i > $o) > $i > $i > $i > $i > $o). 0.18/0.50 thf(func_def_98, type, indeq: $i > ($i > $i > $o) > $i > $i > $i > $i). 0.18/0.50 thf(func_def_99, type, fixfu2: $i > ($i > $i > $o) > $i > $i > $o). 0.18/0.50 thf(func_def_100, type, d_11_i: $i > ($i > $i > $o) > $i > $i > $i > $i). 0.18/0.50 thf(func_def_101, type, indeq2: $i > ($i > $i > $o) > $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_103, type, n_is: $i > $i > $o). 0.18/0.50 thf(func_def_104, type, nis: $i > $i > $o). 0.18/0.50 thf(func_def_105, type, n_in: $i > $i > $o). 0.18/0.50 thf(func_def_106, type, n_some: ($i > $o) > $o). 0.18/0.50 thf(func_def_107, type, n_all: ($i > $o) > $o). 0.18/0.50 thf(func_def_108, type, n_one: ($i > $o) > $o). 0.18/0.50 thf(func_def_110, type, cond1: $i > $o). 0.18/0.50 thf(func_def_111, type, cond2: $i > $o). 0.18/0.50 thf(func_def_112, type, i1_s: ($i > $o) > $i). 0.18/0.50 thf(func_def_113, type, d_22_prop1: $i > $o). 0.18/0.50 thf(func_def_114, type, d_23_prop1: $i > $o). 0.18/0.50 thf(func_def_115, type, d_24_prop1: $i > $o). 0.18/0.50 thf(func_def_116, type, d_24_prop2: $i > $i > $o). 0.18/0.50 thf(func_def_117, type, prop3: $i > $i > $i > $o). 0.18/0.50 thf(func_def_118, type, prop4: $i > $o). 0.18/0.50 thf(func_def_119, type, d_24_g: $i > $i). 0.18/0.50 thf(func_def_120, type, plus: $i > $i). 0.18/0.50 thf(func_def_121, type, n_pl: $i > $i > $i). 0.18/0.50 thf(func_def_122, type, d_25_prop1: $i > $i > $i > $o). 0.18/0.50 thf(func_def_123, type, d_26_prop1: $i > $i > $o). 0.18/0.50 thf(func_def_124, type, d_27_prop1: $i > $i > $o). 0.18/0.50 thf(func_def_125, type, d_28_prop1: $i > $i > $i > $o). 0.18/0.50 thf(func_def_126, type, diffprop: $i > $i > $i > $o). 0.18/0.50 thf(func_def_127, type, d_29_ii: $i > $i > $o). 0.18/0.50 thf(func_def_128, type, iii: $i > $i > $o). 0.18/0.50 thf(func_def_129, type, d_29_prop1: $i > $i > $o). 0.18/0.50 thf(func_def_130, type, moreis: $i > $i > $o). 0.18/0.50 thf(func_def_131, type, lessis: $i > $i > $o). 0.18/0.50 thf(func_def_150, type, sK0: ($i > $o) > $i). 0.18/0.50 thf(func_def_152, type, sK2: $i > $i > $i > $i > $i). 0.18/0.50 thf(func_def_155, type, ph5: !>[X0: $tType]:(X0)). 0.18/0.50 thf(f1338,plain,( 0.18/0.50 $false), 0.18/0.50 inference(trivial_inequality_removal,[],[f1337])). 0.18/0.50 thf(f1337,plain,( 0.18/0.50 ($true = $false)), 0.18/0.50 inference(backward_demodulation,[],[f1133,f1336])). 0.18/0.50 thf(f1336,plain,( 0.18/0.50 ($false = (n_is @ sK4 @ sK3))), 0.18/0.50 inference(trivial_inequality_removal,[],[f1335])). 0.18/0.50 thf(f1335,plain,( 0.18/0.50 ($false = (n_is @ sK4 @ sK3)) | ($true = $false)), 0.18/0.50 inference(forward_demodulation,[],[f1334,f955])). 0.18/0.50 thf(f955,plain,( 0.18/0.50 ((n_is @ sK3 @ sK4) = $false)), 0.18/0.50 inference(binary_proxy_clausification,[],[f954])). 0.18/0.50 thf(f954,plain,( 0.18/0.50 (((~ (iii @ sK3 @ sK4)) => (n_is @ sK3 @ sK4)) = $false)), 0.18/0.50 inference(not_proxy_clausification,[],[f953])). 0.18/0.50 thf(f953,plain,( 0.18/0.50 ($true = (~ ((~ (iii @ sK3 @ sK4)) => (n_is @ sK3 @ sK4))))), 0.18/0.50 inference(binary_proxy_clausification,[],[f950])). 0.18/0.50 thf(f950,plain,( 0.18/0.50 ($false = ((~ ((~ (iii @ sK3 @ sK4)) => (n_is @ sK3 @ sK4))) => (n_some @ (diffprop @ sK3 @ sK4))))), 0.18/0.50 inference(binary_proxy_clausification,[],[f949])). 0.18/0.50 thf(f949,plain,( 0.18/0.50 (((is_of @ sK4 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => ((~ ((~ (iii @ sK3 @ sK4)) => (n_is @ sK3 @ sK4))) => (n_some @ (diffprop @ sK3 @ sK4)))) = $false)), 0.18/0.50 inference(beta_eta_normalization,[],[f948])). 0.18/0.50 thf(f948,plain,( 0.18/0.50 (((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((~ ((~ (iii @ sK3 @ Y0)) => (n_is @ sK3 @ Y0))) => (n_some @ (diffprop @ sK3 @ Y0))))) @ sK4) = $false)), 0.18/0.50 inference(sigma_clausification,[],[f946])). 0.18/0.50 thf(f946,plain,( 0.18/0.50 ((!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((~ ((~ (iii @ sK3 @ Y0)) => (n_is @ sK3 @ Y0))) => (n_some @ (diffprop @ sK3 @ Y0)))))) = $false)), 0.18/0.50 inference(binary_proxy_clausification,[],[f945])). 0.18/0.50 thf(f945,plain,( 0.18/0.50 (((is_of @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((~ ((~ (iii @ sK3 @ Y0)) => (n_is @ sK3 @ Y0))) => (n_some @ (diffprop @ sK3 @ Y0))))))) = $false)), 0.18/0.50 inference(beta_eta_normalization,[],[f944])). 0.18/0.50 thf(f944,plain,( 0.18/0.50 (((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((~ ((~ (iii @ Y0 @ Y1)) => (n_is @ Y0 @ Y1))) => (n_some @ (diffprop @ Y0 @ Y1)))))))) @ sK3) = $false)), 0.18/0.50 inference(sigma_clausification,[],[f943])). 0.18/0.50 thf(f943,plain,( 0.18/0.50 ($true != (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((~ ((~ (iii @ Y0 @ Y1)) => (n_is @ Y0 @ Y1))) => (n_some @ (diffprop @ Y0 @ Y1))))))))))), 0.18/0.50 inference(boolean_simplification,[],[f942])). 0.18/0.50 thf(f942,plain,( 0.18/0.50 ($true != (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((~ (((iii @ Y0 @ Y1) => $false) => (n_is @ Y0 @ Y1))) => (n_some @ (diffprop @ Y0 @ Y1))))))))))), 0.18/0.50 inference(boolean_simplification,[],[f941])). 0.18/0.50 thf(f941,plain,( 0.18/0.50 ((!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => (((((iii @ Y0 @ Y1) => $false) => (n_is @ Y0 @ Y1)) => $false) => (n_some @ (diffprop @ Y0 @ Y1))))))))) != $true)), 0.18/0.50 inference(beta_eta_normalization,[],[f646])). 0.18/0.50 thf(f646,plain,( 0.18/0.50 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((is_of @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))) @ (iii @ Y2 @ Y3) @ (n_is @ Y2 @ Y3))))) @ Y0 @ Y1)) => ((^[Y2 : $i]: ((^[Y3 : $i]: (n_some @ (diffprop @ Y2 @ Y3))))) @ Y0 @ Y1)))))))), 0.18/0.50 inference(definition_unfolding,[],[f577,f581,f581,f624,f627,f594])). 0.18/0.50 thf(f594,plain,( 0.18/0.50 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))), 0.18/0.50 inference(cnf_transformation,[],[f295])). 0.18/0.50 thf(f295,plain,( 0.18/0.50 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))), 0.18/0.50 inference(fool_elimination,[],[f186])). 0.18/0.50 thf(f186,axiom,( 0.18/0.50 ((^[X0 : $i, X1 : $i] : (n_some @ (diffprop @ X0 @ X1))) = d_29_ii)), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_d_29_ii)). 0.18/0.50 thf(f627,plain,( 0.18/0.50 (lessis = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ Y3 @ $false)) @ Y2))) @ (iii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))), 0.18/0.50 inference(definition_unfolding,[],[f615,f625])). 0.18/0.50 thf(f625,plain,( 0.18/0.50 (l_or = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (Y2 => Y3)))) @ Y1 @ $false)) @ Y0))))), 0.18/0.50 inference(definition_unfolding,[],[f570,f598,f624])). 0.18/0.50 thf(f598,plain,( 0.18/0.50 (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))), 0.18/0.50 inference(cnf_transformation,[],[f437])). 0.18/0.50 thf(f437,plain,( 0.18/0.50 (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))), 0.18/0.50 inference(fool_elimination,[],[f436])). 0.18/0.50 thf(f436,plain,( 0.18/0.50 ((^[X0 : $o, X1 : $o] : (X0 => X1)) = imp)), 0.18/0.50 inference(rectify,[],[f33])). 0.18/0.50 thf(f33,axiom,( 0.18/0.50 ((^[X0 : $o, X1 : $o] : (X0 => X1)) = imp)), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_imp)). 0.18/0.50 thf(f570,plain,( 0.18/0.50 (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))), 0.18/0.50 inference(cnf_transformation,[],[f466])). 0.18/0.50 thf(f466,plain,( 0.18/0.50 (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))), 0.18/0.50 inference(fool_elimination,[],[f39])). 0.18/0.50 thf(f39,axiom,( 0.18/0.50 (l_or = (^[X0 : $o] : (imp @ (d_not @ X0))))), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_l_or)). 0.18/0.50 thf(f615,plain,( 0.18/0.50 (lessis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (iii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))), 0.18/0.50 inference(cnf_transformation,[],[f505])). 0.18/0.50 thf(f505,plain,( 0.18/0.50 (lessis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (iii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))), 0.18/0.50 inference(fool_elimination,[],[f190])). 0.18/0.50 thf(f190,axiom,( 0.18/0.50 ((^[X0 : $i, X1 : $i] : (l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))) = lessis)), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_lessis)). 0.18/0.50 thf(f624,plain,( 0.18/0.50 (d_not = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ Y0 @ $false)))), 0.18/0.50 inference(definition_unfolding,[],[f569,f598])). 0.18/0.50 thf(f569,plain,( 0.18/0.50 (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))), 0.18/0.50 inference(cnf_transformation,[],[f240])). 0.18/0.50 thf(f240,plain,( 0.18/0.50 (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))), 0.18/0.50 inference(fool_elimination,[],[f34])). 0.18/0.50 thf(f34,axiom,( 0.18/0.50 ((^[X0 : $o] : (imp @ X0 @ $false)) = d_not)), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_d_not)). 0.18/0.50 thf(f581,plain,( 0.18/0.50 (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))))), 0.18/0.50 inference(cnf_transformation,[],[f401])). 0.18/0.50 thf(f401,plain,( 0.18/0.50 (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))))), 0.18/0.50 inference(fool_elimination,[],[f400])). 0.18/0.50 thf(f400,plain,( 0.18/0.50 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((is_of @ X2 @ X0) => (X1 @ X2)))) = all_of)), 0.18/0.50 inference(rectify,[],[f2])). 0.18/0.50 thf(f2,axiom,( 0.18/0.50 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((is_of @ X2 @ X0) => (X1 @ X2)))) = all_of)), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_all_of)). 0.18/0.50 thf(f577,plain,( 0.18/0.50 ($true != (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_not @ (lessis @ Y0 @ Y1)) => (d_29_ii @ Y0 @ Y1)))))))), 0.18/0.50 inference(cnf_transformation,[],[f561])). 0.18/0.50 thf(f561,plain,( 0.18/0.50 ($true != (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_not @ (lessis @ Y0 @ Y1)) => (d_29_ii @ Y0 @ Y1)))))))), 0.18/0.50 inference(flattening,[],[f513])). 0.18/0.50 thf(f513,plain,( 0.18/0.50 ~($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_not @ (lessis @ Y0 @ Y1)) => (d_29_ii @ Y0 @ Y1)))))))), 0.18/0.50 inference(fool_elimination,[],[f512])). 0.18/0.50 thf(f512,plain,( 0.18/0.50 ~(all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ nat)) @ (^[X3 : $i] : ((d_not @ (lessis @ X1 @ X3)) => (d_29_ii @ X1 @ X3))))))), 0.18/0.50 inference(rectify,[],[f201])). 0.18/0.50 thf(f201,negated_conjecture,( 0.18/0.50 ~(all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : ((d_not @ (lessis @ X0 @ X1)) => (d_29_ii @ X0 @ X1))))))), 0.18/0.50 inference(negated_conjecture,[],[f200])). 0.18/0.50 thf(f200,conjecture,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : ((d_not @ (lessis @ X0 @ X1)) => (d_29_ii @ X0 @ X1))))))), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10k)). 0.18/0.50 thf(f1334,plain,( 0.18/0.50 ((n_is @ sK3 @ sK4) = $true) | ($false = (n_is @ sK4 @ sK3))), 0.18/0.50 inference(trivial_inequality_removal,[],[f1333])). 0.18/0.50 thf(f1333,plain,( 0.18/0.50 ($true = $false) | ((n_is @ sK3 @ sK4) = $true) | ($false = (n_is @ sK4 @ sK3))), 0.18/0.50 inference(forward_demodulation,[],[f1330,f957])). 0.18/0.50 thf(f957,plain,( 0.18/0.50 ((iii @ sK3 @ sK4) = $false)), 0.18/0.50 inference(not_proxy_clausification,[],[f956])). 0.18/0.50 thf(f956,plain,( 0.18/0.50 ((~ (iii @ sK3 @ sK4)) = $true)), 0.18/0.50 inference(binary_proxy_clausification,[],[f954])). 0.18/0.50 thf(f1330,plain,( 0.18/0.50 ($true = (iii @ sK3 @ sK4)) | ((n_is @ sK3 @ sK4) = $true) | ($false = (n_is @ sK4 @ sK3))), 0.18/0.50 inference(trivial_inequality_removal,[],[f1328])). 0.18/0.50 thf(f1328,plain,( 0.18/0.50 ($false = (n_is @ sK4 @ sK3)) | ($true = $false) | ($true = (iii @ sK3 @ sK4)) | ((n_is @ sK3 @ sK4) = $true)), 0.18/0.50 inference(superposition,[],[f951,f1174])). 0.18/0.50 thf(f1174,plain,( 0.18/0.50 ( ! [X0 : $i] : (((is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ nat))) = $false) | ((iii @ sK3 @ X0) = $true) | ((n_is @ X0 @ sK3) = $false) | ($true = (n_is @ sK3 @ X0))) )), 0.18/0.50 inference(trivial_inequality_removal,[],[f1166])). 0.18/0.50 thf(f1166,plain,( 0.18/0.50 ( ! [X0 : $i] : (((is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ nat))) = $false) | ((n_is @ X0 @ sK3) = $false) | ((iii @ sK3 @ X0) = $true) | ($true = (n_is @ sK3 @ X0)) | ($true = $false)) )), 0.18/0.50 inference(superposition,[],[f800,f947])). 0.18/0.50 thf(f947,plain,( 0.18/0.50 ($true = (is_of @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ nat))))), 0.18/0.50 inference(binary_proxy_clausification,[],[f945])). 0.18/0.50 thf(f800,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = (iii @ X2 @ X1)) | ((n_is @ X2 @ X1) = $true) | ((n_is @ X1 @ X2) = $false)) )), 0.18/0.50 inference(not_proxy_clausification,[],[f796])). 0.18/0.50 thf(f796,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (((n_is @ X2 @ X1) = $true) | ((n_is @ X1 @ X2) = $false) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ((~ (iii @ X2 @ X1)) = $false)) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f795])). 0.18/0.50 thf(f795,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : ((((~ (n_some @ (diffprop @ X1 @ X2))) => (n_is @ X1 @ X2)) = $false) | ((~ (iii @ X2 @ X1)) = $false) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ((n_is @ X2 @ X1) = $true)) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f794])). 0.18/0.50 thf(f794,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (iii @ X2 @ X1)) => (n_is @ X2 @ X1))) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | (((~ (n_some @ (diffprop @ X1 @ X2))) => (n_is @ X1 @ X2)) = $false) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f793])). 0.18/0.50 thf(f793,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($true = (((~ (n_some @ (diffprop @ X1 @ X2))) => (n_is @ X1 @ X2)) => ((~ (iii @ X2 @ X1)) => (n_is @ X2 @ X1)))) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f792])). 0.18/0.50 thf(f792,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($true = ((is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => (((~ (n_some @ (diffprop @ X1 @ X2))) => (n_is @ X1 @ X2)) => ((~ (iii @ X2 @ X1)) => (n_is @ X2 @ X1))))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(beta_eta_normalization,[],[f791])). 0.18/0.50 thf(f791,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (((~ (n_some @ (diffprop @ X1 @ Y0))) => (n_is @ X1 @ Y0)) => ((~ (iii @ Y0 @ X1)) => (n_is @ Y0 @ X1))))) @ X2) = $true) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(pi_clausification,[],[f790])). 0.18/0.50 thf(f790,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (((~ (n_some @ (diffprop @ X1 @ Y0))) => (n_is @ X1 @ Y0)) => ((~ (iii @ Y0 @ X1)) => (n_is @ Y0 @ X1))))))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f789])). 0.18/0.50 thf(f789,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = ((is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (((~ (n_some @ (diffprop @ X1 @ Y0))) => (n_is @ X1 @ Y0)) => ((~ (iii @ Y0 @ X1)) => (n_is @ Y0 @ X1))))))))) )), 0.18/0.50 inference(beta_eta_normalization,[],[f788])). 0.18/0.50 thf(f788,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => (((~ (n_some @ (diffprop @ Y0 @ Y1))) => (n_is @ Y0 @ Y1)) => ((~ (iii @ Y1 @ Y0)) => (n_is @ Y1 @ Y0)))))))) @ X1))) )), 0.18/0.50 inference(pi_clausification,[],[f787])). 0.18/0.50 thf(f787,plain,( 0.18/0.50 ((!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => (((~ (n_some @ (diffprop @ Y0 @ Y1))) => (n_is @ Y0 @ Y1)) => ((~ (iii @ Y1 @ Y0)) => (n_is @ Y1 @ Y0))))))))) = $true)), 0.18/0.50 inference(boolean_simplification,[],[f786])). 0.18/0.50 thf(f786,plain,( 0.18/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((((n_some @ (diffprop @ Y0 @ Y1)) => $false) => (n_is @ Y0 @ Y1)) => ((~ (iii @ Y1 @ Y0)) => (n_is @ Y1 @ Y0))))))))))), 0.18/0.50 inference(boolean_simplification,[],[f785])). 0.18/0.50 thf(f785,plain,( 0.18/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((((n_some @ (diffprop @ Y0 @ Y1)) => $false) => (n_is @ Y0 @ Y1)) => (((iii @ Y1 @ Y0) => $false) => (n_is @ Y1 @ Y0))))))))))), 0.18/0.50 inference(beta_eta_normalization,[],[f644])). 0.18/0.50 thf(f644,plain,( 0.18/0.50 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((is_of @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (n_some @ (diffprop @ Y4 @ Y5))))) @ Y2 @ Y3) @ (n_is @ Y2 @ Y3))))) @ Y0 @ Y1) => ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))) @ (iii @ Y2 @ Y3) @ (n_is @ Y2 @ Y3))))) @ Y1 @ Y0)))))))), 0.18/0.50 inference(definition_unfolding,[],[f575,f581,f581,f626,f627])). 0.18/0.50 thf(f626,plain,( 0.18/0.50 (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ Y3 @ $false)) @ Y2))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (n_some @ (diffprop @ Y2 @ Y3))))) @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))), 0.18/0.50 inference(definition_unfolding,[],[f593,f625,f594])). 0.18/0.50 thf(f593,plain,( 0.18/0.50 (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (d_29_ii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))), 0.18/0.50 inference(cnf_transformation,[],[f540])). 0.18/0.50 thf(f540,plain,( 0.18/0.50 (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (d_29_ii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))), 0.18/0.50 inference(fool_elimination,[],[f189])). 0.18/0.50 thf(f189,axiom,( 0.18/0.50 ((^[X0 : $i, X1 : $i] : (l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))) = moreis)), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_moreis)). 0.18/0.50 thf(f575,plain,( 0.18/0.50 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((moreis @ Y0 @ Y1) => (lessis @ Y1 @ Y0)))))))), 0.18/0.50 inference(cnf_transformation,[],[f535])). 0.18/0.50 thf(f535,plain,( 0.18/0.50 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((moreis @ Y0 @ Y1) => (lessis @ Y1 @ Y0)))))))), 0.18/0.50 inference(fool_elimination,[],[f534])). 0.18/0.50 thf(f534,plain,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ nat)) @ (^[X3 : $i] : ((moreis @ X1 @ X3) => (lessis @ X3 @ X1))))))), 0.18/0.50 inference(rectify,[],[f220])). 0.18/0.50 thf(f220,axiom,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : ((moreis @ X0 @ X1) => (lessis @ X1 @ X0))))))), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13)). 0.18/0.50 thf(f951,plain,( 0.18/0.50 ($true = (is_of @ sK4 @ (^[Y0 : $i]: (in @ Y0 @ nat))))), 0.18/0.50 inference(binary_proxy_clausification,[],[f949])). 0.18/0.50 thf(f1133,plain,( 0.18/0.50 ($true = (n_is @ sK4 @ sK3))), 0.18/0.50 inference(trivial_inequality_removal,[],[f1132])). 0.18/0.50 thf(f1132,plain,( 0.18/0.50 ($true = $false) | ($true = (n_is @ sK4 @ sK3))), 0.18/0.50 inference(forward_demodulation,[],[f1131,f1071])). 0.18/0.50 thf(f1071,plain,( 0.18/0.50 ((n_some @ (diffprop @ sK4 @ sK3)) = $false)), 0.18/0.50 inference(trivial_inequality_removal,[],[f1070])). 0.18/0.50 thf(f1070,plain,( 0.18/0.50 ((n_some @ (diffprop @ sK4 @ sK3)) = $false) | ($true = $false)), 0.18/0.50 inference(forward_demodulation,[],[f1069,f957])). 0.18/0.50 thf(f1069,plain,( 0.18/0.50 ($true = (iii @ sK3 @ sK4)) | ((n_some @ (diffprop @ sK4 @ sK3)) = $false)), 0.18/0.50 inference(trivial_inequality_removal,[],[f1065])). 0.18/0.50 thf(f1065,plain,( 0.18/0.50 ($true = $false) | ((n_some @ (diffprop @ sK4 @ sK3)) = $false) | ($true = (iii @ sK3 @ sK4))), 0.18/0.50 inference(superposition,[],[f951,f999])). 0.18/0.50 thf(f999,plain,( 0.18/0.50 ( ! [X0 : $i] : (((is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ nat))) = $false) | ((iii @ sK3 @ X0) = $true) | ((n_some @ (diffprop @ X0 @ sK3)) = $false)) )), 0.18/0.50 inference(trivial_inequality_removal,[],[f994])). 0.18/0.50 thf(f994,plain,( 0.18/0.50 ( ! [X0 : $i] : (((is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ nat))) = $false) | ((iii @ sK3 @ X0) = $true) | ($true = $false) | ((n_some @ (diffprop @ X0 @ sK3)) = $false)) )), 0.18/0.50 inference(superposition,[],[f873,f947])). 0.18/0.50 thf(f873,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (n_some @ (diffprop @ X1 @ X2))) | ($true = (iii @ X2 @ X1))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f872])). 0.18/0.50 thf(f872,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = ((n_some @ (diffprop @ X1 @ X2)) => (iii @ X2 @ X1))) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f871])). 0.18/0.50 thf(f871,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($true = ((is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => ((n_some @ (diffprop @ X1 @ X2)) => (iii @ X2 @ X1)))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(beta_eta_normalization,[],[f870])). 0.18/0.50 thf(f870,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = ((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((n_some @ (diffprop @ X1 @ Y0)) => (iii @ Y0 @ X1)))) @ X2))) )), 0.18/0.50 inference(pi_clausification,[],[f869])). 0.18/0.50 thf(f869,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((n_some @ (diffprop @ X1 @ Y0)) => (iii @ Y0 @ X1)))))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f868])). 0.18/0.50 thf(f868,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = ((is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((n_some @ (diffprop @ X1 @ Y0)) => (iii @ Y0 @ X1)))))))) )), 0.18/0.50 inference(beta_eta_normalization,[],[f867])). 0.18/0.50 thf(f867,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((n_some @ (diffprop @ Y0 @ Y1)) => (iii @ Y1 @ Y0))))))) @ X1))) )), 0.18/0.50 inference(pi_clausification,[],[f866])). 0.18/0.50 thf(f866,plain,( 0.18/0.50 ((!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((n_some @ (diffprop @ Y0 @ Y1)) => (iii @ Y1 @ Y0)))))))) = $true)), 0.18/0.50 inference(beta_eta_normalization,[],[f654])). 0.18/0.50 thf(f654,plain,( 0.18/0.50 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((is_of @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (n_some @ (diffprop @ Y2 @ Y3))))) @ Y0 @ Y1) => (iii @ Y1 @ Y0)))))))), 0.18/0.50 inference(definition_unfolding,[],[f600,f581,f581,f594])). 0.18/0.50 thf(f600,plain,( 0.18/0.50 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_29_ii @ Y0 @ Y1) => (iii @ Y1 @ Y0)))))))), 0.18/0.50 inference(cnf_transformation,[],[f360])). 0.18/0.50 thf(f360,plain,( 0.18/0.50 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_29_ii @ Y0 @ Y1) => (iii @ Y1 @ Y0)))))))), 0.18/0.50 inference(fool_elimination,[],[f359])). 0.18/0.50 thf(f359,plain,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ nat)) @ (^[X3 : $i] : ((d_29_ii @ X1 @ X3) => (iii @ X3 @ X1))))))), 0.18/0.50 inference(rectify,[],[f221])). 0.18/0.50 thf(f221,axiom,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : ((d_29_ii @ X0 @ X1) => (iii @ X1 @ X0))))))), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz11)). 0.18/0.50 thf(f1131,plain,( 0.18/0.50 ($true = (n_some @ (diffprop @ sK4 @ sK3))) | ($true = (n_is @ sK4 @ sK3))), 0.18/0.50 inference(trivial_inequality_removal,[],[f1130])). 0.18/0.50 thf(f1130,plain,( 0.18/0.50 ($true = (n_some @ (diffprop @ sK4 @ sK3))) | ($true = $false) | ($true = (n_is @ sK4 @ sK3))), 0.18/0.50 inference(forward_demodulation,[],[f1129,f1093])). 0.18/0.50 thf(f1093,plain,( 0.18/0.50 ((iii @ sK4 @ sK3) = $false)), 0.18/0.50 inference(trivial_inequality_removal,[],[f1092])). 0.18/0.50 thf(f1092,plain,( 0.18/0.50 ((iii @ sK4 @ sK3) = $false) | ($true = $false)), 0.18/0.50 inference(forward_demodulation,[],[f1088,f952])). 0.18/0.50 thf(f952,plain,( 0.18/0.50 ((n_some @ (diffprop @ sK3 @ sK4)) = $false)), 0.18/0.50 inference(binary_proxy_clausification,[],[f950])). 0.18/0.50 thf(f1088,plain,( 0.18/0.50 ((iii @ sK4 @ sK3) = $false) | ($true = (n_some @ (diffprop @ sK3 @ sK4)))), 0.18/0.50 inference(trivial_inequality_removal,[],[f1085])). 0.18/0.50 thf(f1085,plain,( 0.18/0.50 ($true = (n_some @ (diffprop @ sK3 @ sK4))) | ((iii @ sK4 @ sK3) = $false) | ($true = $false)), 0.18/0.50 inference(superposition,[],[f951,f1005])). 0.18/0.50 thf(f1005,plain,( 0.18/0.50 ( ! [X0 : $i] : (((is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ nat))) = $false) | ($true = (n_some @ (diffprop @ sK3 @ X0))) | ((iii @ X0 @ sK3) = $false)) )), 0.18/0.50 inference(trivial_inequality_removal,[],[f1000])). 0.18/0.50 thf(f1000,plain,( 0.18/0.50 ( ! [X0 : $i] : (((is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ nat))) = $false) | ($true = (n_some @ (diffprop @ sK3 @ X0))) | ($true = $false) | ((iii @ X0 @ sK3) = $false)) )), 0.18/0.50 inference(superposition,[],[f923,f947])). 0.18/0.50 thf(f923,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = (n_some @ (diffprop @ X2 @ X1))) | ((iii @ X1 @ X2) = $false)) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f922])). 0.18/0.50 thf(f922,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = ((iii @ X1 @ X2) => (n_some @ (diffprop @ X2 @ X1))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f921])). 0.18/0.50 thf(f921,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($true = ((is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => ((iii @ X1 @ X2) => (n_some @ (diffprop @ X2 @ X1))))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(beta_eta_normalization,[],[f920])). 0.18/0.50 thf(f920,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = ((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((iii @ X1 @ Y0) => (n_some @ (diffprop @ Y0 @ X1))))) @ X2))) )), 0.18/0.50 inference(pi_clausification,[],[f919])). 0.18/0.50 thf(f919,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((iii @ X1 @ Y0) => (n_some @ (diffprop @ Y0 @ X1))))))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f918])). 0.18/0.50 thf(f918,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = ((is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((iii @ X1 @ Y0) => (n_some @ (diffprop @ Y0 @ X1))))))))) )), 0.18/0.50 inference(beta_eta_normalization,[],[f917])). 0.18/0.50 thf(f917,plain,( 0.18/0.50 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((iii @ Y0 @ Y1) => (n_some @ (diffprop @ Y1 @ Y0)))))))) @ X1) = $true)) )), 0.18/0.50 inference(pi_clausification,[],[f916])). 0.18/0.50 thf(f916,plain,( 0.18/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((iii @ Y0 @ Y1) => (n_some @ (diffprop @ Y1 @ Y0))))))))))), 0.18/0.50 inference(beta_eta_normalization,[],[f658])). 0.18/0.50 thf(f658,plain,( 0.18/0.50 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((is_of @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((iii @ Y0 @ Y1) => ((^[Y2 : $i]: ((^[Y3 : $i]: (n_some @ (diffprop @ Y2 @ Y3))))) @ Y1 @ Y0)))))) = $true)), 0.18/0.50 inference(definition_unfolding,[],[f606,f581,f581,f594])). 0.18/0.50 thf(f606,plain,( 0.18/0.50 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((iii @ Y0 @ Y1) => (d_29_ii @ Y1 @ Y0)))))))), 0.18/0.50 inference(cnf_transformation,[],[f267])). 0.18/0.50 thf(f267,plain,( 0.18/0.50 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((iii @ Y0 @ Y1) => (d_29_ii @ Y1 @ Y0)))))))), 0.18/0.50 inference(fool_elimination,[],[f266])). 0.18/0.50 thf(f266,plain,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ nat)) @ (^[X3 : $i] : ((iii @ X1 @ X3) => (d_29_ii @ X3 @ X1))))))), 0.18/0.50 inference(rectify,[],[f207])). 0.18/0.50 thf(f207,axiom,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : ((iii @ X0 @ X1) => (d_29_ii @ X1 @ X0))))))), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz12)). 0.18/0.50 thf(f1129,plain,( 0.18/0.50 ($true = (n_is @ sK4 @ sK3)) | ($true = (iii @ sK4 @ sK3)) | ($true = (n_some @ (diffprop @ sK4 @ sK3)))), 0.18/0.50 inference(trivial_inequality_removal,[],[f1125])). 0.18/0.50 thf(f1125,plain,( 0.18/0.50 ($true = $false) | ($true = (n_some @ (diffprop @ sK4 @ sK3))) | ($true = (n_is @ sK4 @ sK3)) | ($true = (iii @ sK4 @ sK3))), 0.18/0.50 inference(superposition,[],[f951,f1010])). 0.18/0.50 thf(f1010,plain,( 0.18/0.50 ( ! [X0 : $i] : (((is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ nat))) = $false) | ($true = (n_some @ (diffprop @ X0 @ sK3))) | ($true = (n_is @ X0 @ sK3)) | ((iii @ X0 @ sK3) = $true)) )), 0.18/0.50 inference(trivial_inequality_removal,[],[f1007])). 0.18/0.50 thf(f1007,plain,( 0.18/0.50 ( ! [X0 : $i] : (((is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ nat))) = $false) | ($true = (n_is @ X0 @ sK3)) | ((iii @ X0 @ sK3) = $true) | ($true = $false) | ($true = (n_some @ (diffprop @ X0 @ sK3)))) )), 0.18/0.50 inference(superposition,[],[f947,f833])). 0.18/0.50 thf(f833,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ((n_is @ X1 @ X2) = $true) | ((iii @ X1 @ X2) = $true) | ($true = (n_some @ (diffprop @ X1 @ X2))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(not_proxy_clausification,[],[f832])). 0.18/0.50 thf(f832,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (((~ (iii @ X1 @ X2)) = $false) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = (n_some @ (diffprop @ X1 @ X2))) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ((n_is @ X1 @ X2) = $true)) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f831])). 0.18/0.50 thf(f831,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($true = (n_some @ (diffprop @ X1 @ X2))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = ((~ (iii @ X1 @ X2)) => (n_is @ X1 @ X2))) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(not_proxy_clausification,[],[f830])). 0.18/0.50 thf(f830,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ((~ (n_some @ (diffprop @ X1 @ X2))) = $false) | ($true = ((~ (iii @ X1 @ X2)) => (n_is @ X1 @ X2)))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f829])). 0.18/0.50 thf(f829,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = ((~ (n_some @ (diffprop @ X1 @ X2))) => ((~ (iii @ X1 @ X2)) => (n_is @ X1 @ X2)))) | ($false = (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f828])). 0.18/0.50 thf(f828,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($true = ((is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => ((~ (n_some @ (diffprop @ X1 @ X2))) => ((~ (iii @ X1 @ X2)) => (n_is @ X1 @ X2))))) | ($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))))) )), 0.18/0.50 inference(beta_eta_normalization,[],[f827])). 0.18/0.50 thf(f827,plain,( 0.18/0.50 ( ! [X2 : $i,X1 : $i] : (($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = ((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((~ (n_some @ (diffprop @ X1 @ Y0))) => ((~ (iii @ X1 @ Y0)) => (n_is @ X1 @ Y0))))) @ X2))) )), 0.18/0.50 inference(pi_clausification,[],[f826])). 0.18/0.50 thf(f826,plain,( 0.18/0.50 ( ! [X1 : $i] : (($false = (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((~ (n_some @ (diffprop @ X1 @ Y0))) => ((~ (iii @ X1 @ Y0)) => (n_is @ X1 @ Y0)))))))) )), 0.18/0.50 inference(binary_proxy_clausification,[],[f825])). 0.18/0.50 thf(f825,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = ((is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ nat))) => (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => ((~ (n_some @ (diffprop @ X1 @ Y0))) => ((~ (iii @ X1 @ Y0)) => (n_is @ X1 @ Y0))))))))) )), 0.18/0.50 inference(beta_eta_normalization,[],[f824])). 0.18/0.50 thf(f824,plain,( 0.18/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((~ (n_some @ (diffprop @ Y0 @ Y1))) => ((~ (iii @ Y0 @ Y1)) => (n_is @ Y0 @ Y1)))))))) @ X1))) )), 0.18/0.50 inference(pi_clausification,[],[f823])). 0.18/0.50 thf(f823,plain,( 0.18/0.50 ((!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => ((~ (n_some @ (diffprop @ Y0 @ Y1))) => ((~ (iii @ Y0 @ Y1)) => (n_is @ Y0 @ Y1))))))))) = $true)), 0.18/0.50 inference(boolean_simplification,[],[f822])). 0.18/0.50 thf(f822,plain,( 0.18/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => (((n_some @ (diffprop @ Y0 @ Y1)) => $false) => ((~ (iii @ Y0 @ Y1)) => (n_is @ Y0 @ Y1))))))))))), 0.18/0.50 inference(boolean_simplification,[],[f821])). 0.18/0.50 thf(f821,plain,( 0.18/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((is_of @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ nat))) => (!! @ $i @ (^[Y1 : $i]: ((is_of @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ nat))) => (((n_some @ (diffprop @ Y0 @ Y1)) => $false) => (((iii @ Y0 @ Y1) => $false) => (n_is @ Y0 @ Y1))))))))))), 0.18/0.50 inference(beta_eta_normalization,[],[f661])). 0.18/0.50 thf(f661,plain,( 0.18/0.50 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((is_of @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (n_some @ (diffprop @ Y2 @ Y3))))) @ Y0 @ Y1)) => ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))) @ (iii @ Y2 @ Y3) @ (n_is @ Y2 @ Y3))))) @ Y0 @ Y1)))))))), 0.18/0.50 inference(definition_unfolding,[],[f610,f581,f581,f624,f594,f627])). 0.18/0.50 thf(f610,plain,( 0.18/0.50 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_not @ (d_29_ii @ Y0 @ Y1)) => (lessis @ Y0 @ Y1)))))))), 0.18/0.50 inference(cnf_transformation,[],[f257])). 0.18/0.50 thf(f257,plain,( 0.18/0.50 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((d_not @ (d_29_ii @ Y0 @ Y1)) => (lessis @ Y0 @ Y1)))))))), 0.18/0.50 inference(fool_elimination,[],[f256])). 0.18/0.50 thf(f256,plain,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ nat)) @ (^[X3 : $i] : ((d_not @ (d_29_ii @ X1 @ X3)) => (lessis @ X1 @ X3))))))), 0.18/0.50 inference(rectify,[],[f209])). 0.18/0.50 thf(f209,axiom,( 0.18/0.50 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : ((d_not @ (d_29_ii @ X0 @ X1)) => (lessis @ X0 @ X1))))))), 0.18/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10e)). 0.18/0.50 % SZS output end Proof for theBenchmark 0.18/0.50 % (15332)------------------------------ 0.18/0.50 % (15332)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.18/0.50 % (15332)Termination reason: Refutation 0.18/0.50 0.18/0.50 % (15332)Memory used [KB]: 6652 0.18/0.50 % (15332)Time elapsed: 0.087 s 0.18/0.50 % (15332)Instructions burned: 176 (million) 0.18/0.50 % (15332)------------------------------ 0.18/0.50 % (15332)------------------------------ 0.18/0.50 % (15318)Success in time 0.151 s 0.18/0.50 % Vampire---4.8 exiting 0.18/0.50 EOF