0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : run_vampire %s %d THM
0.12/0.32	% Computer   : n010.cluster.edu
0.12/0.32	% Model      : x86_64 x86_64
0.12/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.32	% Memory     : 8042.1875MB
0.12/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.32	% CPULimit   : 1920
0.12/0.32	% WCLimit    : 240
0.12/0.32	% DateTime   : Wed Jul 30 03:19:19 EDT 2025
0.12/0.33	% CPUTime    : 
0.12/0.34	This is a THF_ problem
0.12/0.35	Running higher-order theorem proving
0.21/0.39	Running /export/starexec/sandbox/solver/bin/vampire-hol --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --print_def_sorts on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p -m 16384 -t 240
0.25/0.43	% (7944)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_7833 for (2399ds/2Mi)
0.25/0.43	% (7946)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_7833 for (2399ds/275Mi)
0.25/0.43	% (7941)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_7833 for (2399ds/183Mi)
0.25/0.43	% (7943)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_7833 for (2399ds/27Mi)
0.25/0.43	% (7945)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_7833 for (2399ds/2Mi)
0.25/0.43	% (7947)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_7833 for (2399ds/18Mi)
0.25/0.43	% (7942)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_7833 for (2399ds/4Mi)
0.25/0.44	% (7944)Instruction limit reached!
0.25/0.44	% (7944)------------------------------
0.25/0.44	% (7944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.44	% (7944)Termination reason: Unknown
0.25/0.44	% (7944)Termination phase: shuffling
0.25/0.44	
0.25/0.44	% (7945)Instruction limit reached!
0.25/0.44	% (7945)------------------------------
0.25/0.44	% (7945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.44	% (7945)Termination reason: Unknown
0.25/0.44	% (7945)Termination phase: shuffling
0.25/0.44	
0.25/0.44	% (7945)Memory used [KB]: 1279
0.25/0.44	% (7945)Time elapsed: 0.004 s
0.25/0.44	% (7945)Instructions burned: 3 (million)
0.25/0.44	% (7945)------------------------------
0.25/0.44	% (7945)------------------------------
0.25/0.44	% (7944)Memory used [KB]: 1279
0.25/0.44	% (7944)Time elapsed: 0.004 s
0.25/0.44	% (7944)Instructions burned: 2 (million)
0.25/0.44	% (7944)------------------------------
0.25/0.44	% (7944)------------------------------
0.25/0.44	% (7942)Instruction limit reached!
0.25/0.44	% (7942)------------------------------
0.25/0.44	% (7942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.44	% (7942)Termination reason: Unknown
0.25/0.44	% (7942)Termination phase: shuffling
0.25/0.44	
0.25/0.44	% (7942)Memory used [KB]: 1279
0.25/0.44	% (7942)Time elapsed: 0.004 s
0.25/0.44	% (7942)Instructions burned: 4 (million)
0.25/0.44	% (7942)------------------------------
0.25/0.44	% (7942)------------------------------
0.25/0.44	% (7947)Instruction limit reached!
0.25/0.44	% (7947)------------------------------
0.25/0.44	% (7947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.44	% (7947)Termination reason: Unknown
0.25/0.44	% (7947)Termination phase: shuffling
0.25/0.44	
0.25/0.44	% (7947)Memory used [KB]: 1407
0.25/0.44	% (7947)Time elapsed: 0.013 s
0.25/0.44	% (7947)Instructions burned: 18 (million)
0.25/0.44	% (7947)------------------------------
0.25/0.44	% (7947)------------------------------
0.25/0.45	% (7943)Instruction limit reached!
0.25/0.45	% (7943)------------------------------
0.25/0.45	% (7943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.45	% (7943)Termination reason: Unknown
0.25/0.45	% (7943)Termination phase: Property scanning
0.25/0.45	
0.25/0.45	% (7943)Memory used [KB]: 1535
0.25/0.45	% (7943)Time elapsed: 0.019 s
0.25/0.45	% (7943)Instructions burned: 29 (million)
0.25/0.45	% (7943)------------------------------
0.25/0.45	% (7943)------------------------------
0.25/0.45	% (7948)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_7833 for (2399ds/3Mi)
0.25/0.45	% (7949)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_7833 for (2399ds/37Mi)
0.25/0.45	% (7950)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_7833 for (2399ds/15Mi)
0.25/0.46	% (7948)Instruction limit reached!
0.25/0.46	% (7948)------------------------------
0.25/0.46	% (7948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.46	% (7948)Termination reason: Unknown
0.25/0.46	% (7948)Termination phase: shuffling
0.25/0.46	
0.25/0.46	% (7948)Memory used [KB]: 1279
0.25/0.46	% (7948)Time elapsed: 0.004 s
0.25/0.46	% (7948)Instructions burned: 3 (million)
0.25/0.46	% (7948)------------------------------
0.25/0.46	% (7948)------------------------------
0.25/0.46	% (7951)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_7833 for (2399ds/3Mi)
0.25/0.46	% (7950)Instruction limit reached!
0.25/0.46	% (7950)------------------------------
0.25/0.46	% (7950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.46	% (7950)Termination reason: Unknown
0.25/0.46	% (7950)Termination phase: shuffling
0.25/0.46	
0.25/0.46	% (7950)Memory used [KB]: 1407
0.25/0.46	% (7950)Time elapsed: 0.012 s
0.25/0.46	% (7950)Instructions burned: 16 (million)
0.25/0.46	% (7950)------------------------------
0.25/0.46	% (7950)------------------------------
0.25/0.46	% (7951)Instruction limit reached!
0.25/0.46	% (7951)------------------------------
0.25/0.46	% (7951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.46	% (7951)Termination reason: Unknown
0.25/0.46	% (7951)Termination phase: shuffling
0.25/0.46	
0.25/0.46	% (7951)Memory used [KB]: 1279
0.25/0.46	% (7951)Time elapsed: 0.004 s
0.25/0.46	% (7951)Instructions burned: 4 (million)
0.25/0.46	% (7951)------------------------------
0.25/0.46	% (7951)------------------------------
0.25/0.47	% (7952)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_7833 for (2399ds/1041Mi)
0.25/0.47	% (7949)Instruction limit reached!
0.25/0.47	% (7949)------------------------------
0.25/0.47	% (7949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.47	% (7949)Termination reason: Unknown
0.25/0.47	% (7949)Termination phase: shuffling
0.25/0.47	
0.25/0.47	% (7949)Memory used [KB]: 1791
0.25/0.47	% (7949)Time elapsed: 0.020 s
0.25/0.47	% (7949)Instructions burned: 37 (million)
0.25/0.47	% (7949)------------------------------
0.25/0.47	% (7949)------------------------------
0.25/0.47	% (7953)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_7833 for (2399ds/7Mi)
0.25/0.48	% (7953)Instruction limit reached!
0.25/0.48	% (7953)------------------------------
0.25/0.48	% (7953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.48	% (7953)Termination reason: Unknown
0.25/0.48	% (7953)Termination phase: shuffling
0.25/0.48	
0.25/0.48	% (7953)Memory used [KB]: 1407
0.25/0.48	% (7953)Time elapsed: 0.006 s
0.25/0.48	% (7953)Instructions burned: 7 (million)
0.25/0.48	% (7953)------------------------------
0.25/0.48	% (7953)------------------------------
0.25/0.48	% (7955)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_7833 for (2399ds/3Mi)
0.25/0.48	% (7955)Instruction limit reached!
0.25/0.48	% (7955)------------------------------
0.25/0.48	% (7955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.48	% (7955)Termination reason: Unknown
0.25/0.48	% (7955)Termination phase: shuffling
0.25/0.48	
0.25/0.48	% (7955)Memory used [KB]: 1279
0.25/0.48	% (7955)Time elapsed: 0.003 s
0.25/0.48	% (7955)Instructions burned: 5 (million)
0.25/0.48	% (7955)------------------------------
0.25/0.48	% (7955)------------------------------
0.25/0.48	% (7954)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_7833 for (2399ds/16Mi)
0.25/0.49	% (7956)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_7833 for (2399ds/3Mi)
0.25/0.49	% (7958)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_7833 for (2399ds/3Mi)
0.25/0.49	% (7958)Instruction limit reached!
0.25/0.49	% (7958)------------------------------
0.25/0.49	% (7958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.49	% (7958)Termination reason: Unknown
0.25/0.49	% (7958)Termination phase: shuffling
0.25/0.49	
0.25/0.49	% (7958)Memory used [KB]: 1279
0.25/0.49	% (7958)Time elapsed: 0.003 s
0.25/0.49	% (7958)Instructions burned: 4 (million)
0.25/0.49	% (7958)------------------------------
0.25/0.49	% (7958)------------------------------
0.25/0.49	% (7956)Instruction limit reached!
0.25/0.49	% (7956)------------------------------
0.25/0.49	% (7956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.49	% (7956)Termination reason: Unknown
0.25/0.49	% (7956)Termination phase: shuffling
0.25/0.49	
0.25/0.49	% (7956)Memory used [KB]: 1279
0.25/0.49	% (7956)Time elapsed: 0.004 s
0.25/0.49	% (7956)Instructions burned: 3 (million)
0.25/0.49	% (7956)------------------------------
0.25/0.49	% (7956)------------------------------
0.25/0.49	% (7954)Instruction limit reached!
0.25/0.49	% (7954)------------------------------
0.25/0.49	% (7954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.49	% (7954)Termination reason: Unknown
0.25/0.49	% (7954)Termination phase: shuffling
0.25/0.49	
0.25/0.49	% (7954)Memory used [KB]: 1407
0.25/0.49	% (7954)Time elapsed: 0.012 s
0.25/0.49	% (7954)Instructions burned: 16 (million)
0.25/0.49	% (7954)------------------------------
0.25/0.49	% (7954)------------------------------
0.25/0.49	% (7957)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_7833 for (2399ds/7Mi)
0.25/0.50	% (7957)Instruction limit reached!
0.25/0.50	% (7957)------------------------------
0.25/0.50	% (7957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.50	% (7957)Termination reason: Unknown
0.25/0.50	% (7957)Termination phase: shuffling
0.25/0.50	
0.25/0.50	% (7957)Memory used [KB]: 1279
0.25/0.50	% (7957)Time elapsed: 0.006 s
0.25/0.50	% (7957)Instructions burned: 7 (million)
0.25/0.50	% (7957)------------------------------
0.25/0.50	% (7957)------------------------------
0.25/0.50	% (7959)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_7833 for (2399ds/4Mi)
0.25/0.50	% (7959)Instruction limit reached!
0.25/0.50	% (7959)------------------------------
0.25/0.50	% (7959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.50	% (7959)Termination reason: Unknown
0.25/0.50	% (7959)Termination phase: shuffling
0.25/0.50	
0.25/0.50	% (7959)Memory used [KB]: 1279
0.25/0.50	% (7959)Time elapsed: 0.003 s
0.25/0.50	% (7959)Instructions burned: 4 (million)
0.25/0.50	% (7959)------------------------------
0.25/0.50	% (7959)------------------------------
0.25/0.51	% (7960)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_7833 for (2399ds/18Mi)
0.25/0.51	% (7961)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_7833 for (2399ds/710Mi)
0.25/0.51	% (7963)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_7833 for (2398ds/902Mi)
0.25/0.52	% (7962)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_7833 for (2398ds/6Mi)
0.25/0.52	% (7960)Instruction limit reached!
0.25/0.52	% (7960)------------------------------
0.25/0.52	% (7960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.52	% (7960)Termination reason: Unknown
0.25/0.52	% (7960)Termination phase: shuffling
0.25/0.52	
0.25/0.52	% (7960)Memory used [KB]: 1407
0.25/0.52	% (7960)Time elapsed: 0.013 s
0.25/0.52	% (7960)Instructions burned: 18 (million)
0.25/0.52	% (7960)------------------------------
0.25/0.52	% (7960)------------------------------
0.25/0.52	% (7962)Instruction limit reached!
0.25/0.52	% (7962)------------------------------
0.25/0.52	% (7962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.52	% (7962)Termination reason: Unknown
0.25/0.52	% (7962)Termination phase: shuffling
0.25/0.52	
0.25/0.52	% (7962)Memory used [KB]: 1279
0.25/0.52	% (7962)Time elapsed: 0.006 s
0.25/0.52	% (7962)Instructions burned: 7 (million)
0.25/0.52	% (7962)------------------------------
0.25/0.52	% (7962)------------------------------
0.25/0.53	% (7941)Instruction limit reached!
0.25/0.53	% (7941)------------------------------
0.25/0.53	% (7941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.53	% (7941)Termination reason: Unknown
0.25/0.53	% (7941)Termination phase: Saturation
0.25/0.53	
0.25/0.53	% (7941)Memory used [KB]: 6652
0.25/0.53	% (7941)Time elapsed: 0.100 s
0.25/0.53	% (7941)Instructions burned: 183 (million)
0.25/0.53	% (7941)------------------------------
0.25/0.53	% (7941)------------------------------
0.25/0.54	% (7964)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_7833 for (2398ds/21Mi)
0.25/0.54	% (7965)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_7833 for (2398ds/5Mi)
0.25/0.54	% (7965)Instruction limit reached!
0.25/0.54	% (7965)------------------------------
0.25/0.54	% (7965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.54	% (7965)Termination reason: Unknown
0.25/0.54	% (7965)Termination phase: shuffling
0.25/0.54	
0.25/0.54	% (7965)Memory used [KB]: 1279
0.25/0.54	% (7965)Time elapsed: 0.005 s
0.25/0.54	% (7965)Instructions burned: 6 (million)
0.25/0.54	% (7965)------------------------------
0.25/0.54	% (7965)------------------------------
0.25/0.54	% (7964)Instruction limit reached!
0.25/0.54	% (7964)------------------------------
0.25/0.54	% (7964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.54	% (7964)Termination reason: Unknown
0.25/0.54	% (7964)Termination phase: shuffling
0.25/0.54	
0.25/0.54	% (7964)Memory used [KB]: 1407
0.25/0.54	% (7964)Time elapsed: 0.011 s
0.25/0.54	% (7964)Instructions burned: 23 (million)
0.25/0.54	% (7964)------------------------------
0.25/0.54	% (7964)------------------------------
0.25/0.55	% (7966)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_7833 for (2398ds/6Mi)
0.25/0.55	% (7966)Instruction limit reached!
0.25/0.55	% (7966)------------------------------
0.25/0.55	% (7966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.55	% (7966)Termination reason: Unknown
0.25/0.55	% (7966)Termination phase: shuffling
0.25/0.55	
0.25/0.55	% (7966)Memory used [KB]: 1407
0.25/0.55	% (7966)Time elapsed: 0.005 s
0.25/0.55	% (7966)Instructions burned: 6 (million)
0.25/0.55	% (7966)------------------------------
0.25/0.55	% (7966)------------------------------
0.25/0.56	% (7968)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_7833 for (2398ds/779Mi)
1.17/0.56	% (7967)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_7833 for (2398ds/377Mi)
1.17/0.57	% (7969)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_7833 for (2398ds/19Mi)
1.17/0.57	% (7946)Instruction limit reached!
1.17/0.57	% (7946)------------------------------
1.17/0.57	% (7946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
1.17/0.57	% (7946)Termination reason: Unknown
1.17/0.57	% (7946)Termination phase: Saturation
1.17/0.57	
1.17/0.57	% (7946)Memory used [KB]: 6524
1.17/0.57	% (7946)Time elapsed: 0.137 s
1.17/0.57	% (7946)Instructions burned: 275 (million)
1.17/0.57	% (7946)------------------------------
1.17/0.57	% (7946)------------------------------
1.27/0.57	% (7969)Instruction limit reached!
1.27/0.57	% (7969)------------------------------
1.27/0.57	% (7969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
1.27/0.57	% (7969)Termination reason: Unknown
1.27/0.57	% (7969)Termination phase: shuffling
1.27/0.57	
1.27/0.57	% (7969)Memory used [KB]: 1663
1.27/0.57	% (7969)Time elapsed: 0.007 s
1.27/0.57	% (7969)Instructions burned: 20 (million)
1.27/0.57	% (7969)------------------------------
1.27/0.57	% (7969)------------------------------
1.27/0.58	% (7970)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_7833 for (2398ds/879Mi)
1.27/0.58	% (7971)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_7833 for (2398ds/17Mi)
1.27/0.59	% (7971)Instruction limit reached!
1.27/0.59	% (7971)------------------------------
1.27/0.59	% (7971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
1.27/0.59	% (7971)Termination reason: Unknown
1.27/0.59	% (7971)Termination phase: shuffling
1.27/0.59	
1.27/0.59	% (7971)Memory used [KB]: 1407
1.27/0.59	% (7971)Time elapsed: 0.008 s
1.27/0.59	% (7971)Instructions burned: 17 (million)
1.27/0.59	% (7971)------------------------------
1.27/0.59	% (7971)------------------------------
1.27/0.59	% (7952)First to succeed.
1.27/0.60	% (7972)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_7833 for (2398ds/3Mi)
1.27/0.60	% (7952)Refutation found. Thanks to Tanya!
1.27/0.60	% SZS status Theorem for E---3.1_7833
1.27/0.60	% SZS output start Proof for E---3.1_7833
1.27/0.60	thf(type_def_5, type, partia1833973666xt_a_b: $tType).
1.27/0.60	thf(type_def_6, type, a: $tType).
1.27/0.60	thf(type_def_7, type, set_a: $tType).
1.27/0.60	thf(type_def_9, type, int: $tType).
1.27/0.60	thf(type_def_10, type, product_prod_a_a: $tType).
1.27/0.60	thf(func_def_0, type, partia1833973666xt_a_b: $tType).
1.27/0.60	thf(func_def_1, type, product_prod_a_a: $tType).
1.27/0.60	thf(func_def_2, type, set_a: $tType).
1.27/0.60	thf(func_def_3, type, int: $tType).
1.27/0.60	thf(func_def_4, type, a: $tType).
1.27/0.60	thf(func_def_5, type, a_l_coset_a_b: partia1833973666xt_a_b > a > set_a > set_a).
1.27/0.60	thf(func_def_6, type, additi2104487374up_a_b: set_a > partia1833973666xt_a_b > $o).
1.27/0.60	thf(func_def_7, type, set_add_a_b: partia1833973666xt_a_b > set_a > set_a > set_a).
1.27/0.60	thf(func_def_8, type, partia1066395285xt_a_b: partia1833973666xt_a_b > set_a).
1.27/0.60	thf(func_def_9, type, mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a).
1.27/0.60	thf(func_def_10, type, minus_minus_int: int > int > int).
1.27/0.60	thf(func_def_11, type, minus_minus_set_a: set_a > set_a > set_a).
1.27/0.60	thf(func_def_12, type, plus_plus_int: int > int > int).
1.27/0.60	thf(func_def_13, type, uminus_uminus_int: int > int).
1.27/0.60	thf(func_def_14, type, uminus_uminus_set_a: set_a > set_a).
1.27/0.60	thf(func_def_15, type, locali1648887798ac_a_b: partia1833973666xt_a_b > set_a > $o).
1.27/0.60	thf(func_def_16, type, locali807230110ng_a_b: partia1833973666xt_a_b > set_a > $o).
1.27/0.60	thf(func_def_17, type, locali880295127ng_a_b: partia1833973666xt_a_b > set_a > $o).
1.27/0.60	thf(func_def_18, type, locali425460998xt_a_b: partia1833973666xt_a_b > set_a > $o).
1.27/0.60	thf(func_def_19, type, bot_bot_set_a: set_a).
1.27/0.60	thf(func_def_20, type, ord_less_eq_int: int > int > $o).
1.27/0.60	thf(func_def_21, type, ord_less_eq_set_a: set_a > set_a > $o).
1.27/0.60	thf(func_def_22, type, product_fst_a_a: product_prod_a_a > a).
1.27/0.60	thf(func_def_23, type, product_snd_a_a: product_prod_a_a > a).
1.27/0.60	thf(func_def_24, type, a_inv_a_b: partia1833973666xt_a_b > a > a).
1.27/0.60	thf(func_def_25, type, a_minus_a_b: partia1833973666xt_a_b > a > a > a).
1.27/0.60	thf(func_def_26, type, add_pow_a_b_int: partia1833973666xt_a_b > int > a > a).
1.27/0.60	thf(func_def_27, type, add_a_b: partia1833973666xt_a_b > a > a > a).
1.27/0.60	thf(func_def_28, type, zero_a_b: partia1833973666xt_a_b > a).
1.27/0.60	thf(func_def_29, type, semiring_a_b: partia1833973666xt_a_b > $o).
1.27/0.60	thf(func_def_30, type, collect_a: (a > $o) > set_a).
1.27/0.60	thf(func_def_31, type, member_a: a > set_a > $o).
1.27/0.60	thf(func_def_32, type, r: partia1833973666xt_a_b).
1.27/0.60	thf(func_def_33, type, s: set_a).
1.27/0.60	thf(func_def_34, type, r2: a).
1.27/0.60	thf(func_def_35, type, r3: a).
1.27/0.60	thf(func_def_36, type, s2: a).
1.27/0.60	thf(func_def_37, type, s3: a).
1.27/0.60	thf(func_def_38, type, t: a).
1.27/0.60	thf(func_def_39, type, t2: a).
1.27/0.60	thf(func_def_40, type, x: product_prod_a_a).
1.27/0.60	thf(func_def_41, type, y: product_prod_a_a).
1.27/0.60	thf(func_def_58, type, ph1: !>[X0: $tType]:(X0)).
1.27/0.60	thf(f1247,plain,(
1.27/0.60	  $false),
1.27/0.60	  inference(trivial_inequality_removal,[status(thm)],[f1246])).
1.27/0.60	thf(f1246,plain,(
1.27/0.60	  ($true = $false)),
1.27/0.60	  inference(boolean_simplification,[status(thm)],[f1245])).
1.27/0.60	thf(f1245,plain,(
1.27/0.60	  ((~ $true) = $true)),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1129,f1244])).
1.27/0.60	thf(f1244,plain,(
1.27/0.60	  ($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)))))))))),
1.27/0.60	  inference(boolean_simplification,[status(thm)],[f1243])).
1.27/0.60	thf(f1243,plain,(
1.27/0.60	  ($true = ($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))))))))))),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1128,f1227])).
1.27/0.60	thf(f1227,plain,(
1.27/0.60	  ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) = $true)),
1.27/0.60	  inference(boolean_simplification,[status(thm)],[f1225])).
1.27/0.60	thf(f1225,plain,(
1.27/0.60	  ($true = ($true => (member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r))))),
1.27/0.60	  inference(superposition,[status(thm)],[f1207,f787])).
1.27/0.60	thf(f787,plain,(
1.27/0.60	  ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s) = $true)),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f339])).
1.27/0.60	thf(f339,plain,(
1.27/0.60	  ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s) = $true)),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f338])).
1.27/0.60	thf(f338,plain,(
1.27/0.60	  (member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s)),
1.27/0.60	  inference(rectify,[status(thm)],[f45])).
1.27/0.60	thf(f45,axiom,(
1.27/0.60	  (member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ s)),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_65_f8)).
1.27/0.60	thf(f1207,plain,(
1.27/0.60	  ( ! [X1 : a] : ((((member_a @ X1 @ s) => (member_a @ X1 @ (partia1066395285xt_a_b @ r))) = $true)) )),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f1206])).
1.27/0.60	thf(f1206,plain,(
1.27/0.60	  ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((member_a @ Y0 @ s) => (member_a @ Y0 @ (partia1066395285xt_a_b @ r)))) @ X1))) )),
1.27/0.60	  inference(pi_clausification,[status(thm)],[f1108])).
1.27/0.60	thf(f1108,plain,(
1.27/0.60	  ((!! @ a @ (^[Y0 : a]: ((member_a @ Y0 @ s) => (member_a @ Y0 @ (partia1066395285xt_a_b @ r))))) = $true)),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f1027])).
1.27/0.60	thf(f1027,plain,(
1.27/0.60	  (((^[Y0 : set_a]: ((^[Y1 : set_a]: (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y0) => (member_a @ Y2 @ Y1))))))) @ s @ (partia1066395285xt_a_b @ r)) = $true)),
1.27/0.60	  inference(definition_unfolding,[status(thm)],[f944,f912])).
1.27/0.60	thf(f912,plain,(
1.27/0.60	  (ord_less_eq_set_a = (^[Y0 : set_a]: ((^[Y1 : set_a]: (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y0) => (member_a @ Y2 @ Y1))))))))),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f459])).
1.27/0.60	thf(f459,plain,(
1.27/0.60	  (ord_less_eq_set_a = (^[Y0 : set_a]: ((^[Y1 : set_a]: (!! @ a @ (^[Y2 : a]: ((member_a @ Y2 @ Y0) => (member_a @ Y2 @ Y1))))))))),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f458])).
1.27/0.60	thf(f458,plain,(
1.27/0.60	  ((^[X0 : set_a, X1 : set_a] : (! [X2 : a] : ((member_a @ X2 @ X0) => (member_a @ X2 @ X1)))) = ord_less_eq_set_a)),
1.27/0.60	  inference(rectify,[status(thm)],[f204])).
1.27/0.60	thf(f204,axiom,(
1.27/0.60	  ((^[X41 : set_a, X42 : set_a] : (! [X18 : a] : ((member_a @ X18 @ X41) => (member_a @ X18 @ X42)))) = ord_less_eq_set_a)),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_243_subset__eq)).
1.27/0.60	thf(f944,plain,(
1.27/0.60	  ((ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r)) = $true)),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f595])).
1.27/0.60	thf(f595,plain,(
1.27/0.60	  ((ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r)) = $true)),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f594])).
1.27/0.60	thf(f594,plain,(
1.27/0.60	  (ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r))),
1.27/0.60	  inference(rectify,[status(thm)],[f65])).
1.27/0.60	thf(f65,axiom,(
1.27/0.60	  (ord_less_eq_set_a @ s @ (partia1066395285xt_a_b @ r))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_142_subset)).
1.27/0.60	thf(f1128,plain,(
1.27/0.60	  ($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))))))))))),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1122,f1044])).
1.27/0.60	thf(f1044,plain,(
1.27/0.60	  ((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))))))),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f952])).
1.27/0.60	thf(f952,plain,(
1.27/0.60	  ((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)))))),
1.27/0.60	  inference(definition_unfolding,[status(thm)],[f721,f855])).
1.27/0.60	thf(f855,plain,(
1.27/0.60	  (a_minus_a_b = (^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))))),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f313])).
1.27/0.60	thf(f313,plain,(
1.27/0.60	  (a_minus_a_b = (^[Y0 : partia1833973666xt_a_b]: ((^[Y1 : a]: ((^[Y2 : a]: (add_a_b @ Y0 @ Y1 @ (a_inv_a_b @ Y0 @ Y2))))))))),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f312])).
1.27/0.60	thf(f312,plain,(
1.27/0.60	  (a_minus_a_b = (^[X0 : partia1833973666xt_a_b, X1 : a, X2 : a] : (add_a_b @ X0 @ X1 @ (a_inv_a_b @ X0 @ X2))))),
1.27/0.60	  inference(rectify,[status(thm)],[f165])).
1.27/0.60	thf(f165,axiom,(
1.27/0.60	  (a_minus_a_b = (^[X37 : partia1833973666xt_a_b, X18 : a, X38 : a] : (add_a_b @ X37 @ X18 @ (a_inv_a_b @ X37 @ X38))))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_130_a__minus__def)).
1.27/0.60	thf(f721,plain,(
1.27/0.60	  ((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)))))),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f285])).
1.27/0.60	thf(f285,plain,(
1.27/0.60	  ((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)))))),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f90])).
1.27/0.60	thf(f90,axiom,(
1.27/0.60	  ((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)))))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_58_f7)).
1.27/0.60	thf(f1122,plain,(
1.27/0.60	  ($true = ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y))))))))))),
1.27/0.60	  inference(boolean_simplification,[status(thm)],[f1121])).
1.27/0.60	thf(f1121,plain,(
1.27/0.60	  ($true = ($true => ((member_a @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (partia1066395285xt_a_b @ r)) => ((add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t @ s3) @ (product_snd_a_a @ y)) @ (zero_a_b @ r)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ s2) @ (product_snd_a_a @ x)) @ (mult_a_ring_ext_a_b @ r @ t @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ r3) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s3 @ (product_fst_a_a @ y))))))) = (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ t2 @ t) @ (add_a_b @ r @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))))))))))),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1119,f1073])).
1.27/0.60	thf(f1073,plain,(
1.27/0.60	  ($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)))),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f979])).
1.27/0.60	thf(f979,plain,(
1.27/0.60	  ((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)) = $true)),
1.27/0.60	  inference(definition_unfolding,[status(thm)],[f805,f855])).
1.27/0.60	thf(f805,plain,(
1.27/0.60	  ((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)),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f269])).
1.27/0.60	thf(f269,plain,(
1.27/0.60	  ((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)) = $true)),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f268])).
1.27/0.60	thf(f268,plain,(
1.27/0.60	  (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r))),
1.27/0.60	  inference(rectify,[status(thm)],[f109])).
1.27/0.60	thf(f109,axiom,(
1.27/0.60	  (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s2 @ r3)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_fst_a_a @ y)))) @ (partia1066395285xt_a_b @ r))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_13_f42)).
1.27/0.60	thf(f1119,plain,(
1.27/0.60	  ($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 @ (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))))))) = (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)))))))))))),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1115,f1084])).
1.27/0.60	thf(f1084,plain,(
1.27/0.60	  ((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))))))),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f956])).
1.27/0.60	thf(f956,plain,(
1.27/0.60	  ((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)))))),
1.27/0.60	  inference(definition_unfolding,[status(thm)],[f736,f855])).
1.27/0.60	thf(f736,plain,(
1.27/0.60	  ((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)))))),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f311])).
1.27/0.60	thf(f311,plain,(
1.27/0.60	  ((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)))))),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f232])).
1.27/0.60	thf(f232,axiom,(
1.27/0.60	  ((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)))))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_57_f5)).
1.27/0.60	thf(f1115,plain,(
1.27/0.60	  ($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 @ (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)))))))))))),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1114,f1088])).
1.27/0.60	thf(f1088,plain,(
1.27/0.60	  ((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))))))) = (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))))))))),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f947])).
1.27/0.60	thf(f947,plain,(
1.27/0.60	  ((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)))))))),
1.27/0.60	  inference(definition_unfolding,[status(thm)],[f702,f855,f855,f855,f855])).
1.27/0.60	thf(f702,plain,(
1.27/0.60	  ((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)))))))),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f653])).
1.27/0.60	thf(f653,plain,(
1.27/0.60	  ((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)))))))),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f23])).
1.27/0.60	thf(f23,axiom,(
1.27/0.60	  ((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)))))))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_19_f40)).
1.27/0.60	thf(f1114,plain,(
1.27/0.60	  ($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)))))))))))),
1.27/0.60	  inference(boolean_simplification,[status(thm)],[f1113])).
1.27/0.60	thf(f1113,plain,(
1.27/0.60	  ($true = ($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))))))))))))),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1105,f1094])).
1.27/0.60	thf(f1094,plain,(
1.27/0.60	  ($true = (member_a @ (add_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (a_inv_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)))),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f983])).
1.27/0.60	thf(f983,plain,(
1.27/0.60	  ($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)))),
1.27/0.60	  inference(definition_unfolding,[status(thm)],[f829,f855])).
1.27/0.60	thf(f829,plain,(
1.27/0.60	  ((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)),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f696])).
1.27/0.60	thf(f696,plain,(
1.27/0.60	  ((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)) = $true)),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f695])).
1.27/0.60	thf(f695,plain,(
1.27/0.60	  (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r))),
1.27/0.60	  inference(rectify,[status(thm)],[f81])).
1.27/0.60	thf(f81,axiom,(
1.27/0.60	  (member_a @ (a_minus_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ x) @ (product_snd_a_a @ y)) @ (mult_a_ring_ext_a_b @ r @ s3 @ r2)) @ (mult_a_ring_ext_a_b @ r @ (mult_a_ring_ext_a_b @ r @ s2 @ s3) @ (mult_a_ring_ext_a_b @ r @ (product_snd_a_a @ y) @ (product_fst_a_a @ x)))) @ (partia1066395285xt_a_b @ r))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',fact_12_f41)).
1.27/0.60	thf(f1105,plain,(
1.27/0.60	  ($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))))))))))))),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f1003])).
1.27/0.60	thf(f1003,plain,(
1.27/0.60	  (((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)))))))))) = $true)),
1.27/0.60	  inference(definition_unfolding,[status(thm)],[f880,f855,f855,f855,f855,f855,f855])).
1.27/0.60	thf(f880,plain,(
1.27/0.60	  ($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)))))))))))),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f481])).
1.27/0.60	thf(f481,plain,(
1.27/0.60	  ($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)))))))))))),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f480])).
1.27/0.60	thf(f480,plain,(
1.27/0.60	  (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)))))))))),
1.27/0.60	  inference(rectify,[status(thm)],[f221])).
1.27/0.60	thf(f221,axiom,(
1.27/0.60	  (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)))))))))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.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)).
1.27/0.60	thf(f1129,plain,(
1.27/0.60	  ($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))))))))))),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1117,f1044])).
1.27/0.60	thf(f1117,plain,(
1.27/0.60	  ((~ ((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))))))) = (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))))))))) = $true)),
1.27/0.60	  inference(backward_demodulation,[status(thm)],[f1086,f1084])).
1.27/0.60	thf(f1086,plain,(
1.27/0.60	  ($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))))))))))),
1.27/0.60	  inference(beta_eta_normalization,[status(thm)],[f1022])).
1.27/0.60	thf(f1022,plain,(
1.27/0.60	  ($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)))))))))),
1.27/0.60	  inference(definition_unfolding,[status(thm)],[f936,f855,f855,f855,f855])).
1.27/0.60	thf(f936,plain,(
1.27/0.60	  ((~ ((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)))))))) = $true)),
1.27/0.60	  inference(cnf_transformation,[status(thm)],[f626])).
1.27/0.60	thf(f626,plain,(
1.27/0.60	  ((~ ((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)))))))) = $true)),
1.27/0.60	  inference(fool_elimination,[status(thm)],[f141])).
1.27/0.60	thf(f141,negated_conjecture,(
1.27/0.60	  ~((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)))))))),
1.27/0.60	  inference(negated_conjecture,[status(cth)],[f140])).
1.27/0.60	thf(f140,conjecture,(
1.27/0.60	  ((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)))))))),
1.27/0.60	  file('/export/starexec/sandbox/tmp/tmp.0Pox6o3kGF/E---3.1_7833.p',conj_0)).
1.27/0.60	% SZS output end Proof for E---3.1_7833
1.27/0.60	% (7952)------------------------------
1.27/0.60	% (7952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
1.27/0.60	% (7952)Termination reason: Refutation
1.27/0.60	
1.27/0.60	% (7952)Memory used [KB]: 7547
1.27/0.60	% (7952)Time elapsed: 0.151 s
1.27/0.60	% (7952)Instructions burned: 290 (million)
1.27/0.60	% (7952)------------------------------
1.27/0.60	% (7952)------------------------------
1.27/0.60	% (7940)Success in time 0.207 s
1.27/0.60	EOF