0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : run_vampire %s %d THM 0.11/0.30 % Computer : n032.cluster.edu 0.11/0.30 % Model : x86_64 x86_64 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.30 % Memory : 8042.1875MB 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.30 % CPULimit : 1440 0.11/0.30 % WCLimit : 180 0.11/0.30 % DateTime : Thu Jul 4 08:57:24 EDT 2024 0.11/0.30 % CPUTime : 0.11/0.31 This is a THF_ problem 0.11/0.32 Running higher-order theorem proving 0.16/0.34 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.v8xjebNtRA/E---3.1_26058.p -m 16384 -t 180 0.16/0.36 % (26170)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_26058 for (1799ds/2Mi) 0.16/0.36 % (26168)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_26058 for (1799ds/27Mi) 0.16/0.36 % (26172)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_26058 for (1799ds/18Mi) 0.16/0.36 % (26170)Instruction limit reached! 0.16/0.36 % (26170)------------------------------ 0.16/0.36 % (26170)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.36 % (26170)Termination reason: Unknown 0.16/0.36 % (26170)Termination phase: shuffling 0.16/0.36 0.16/0.36 % (26170)Memory used [KB]: 1279 0.16/0.36 % (26170)Time elapsed: 0.003 s 0.16/0.36 % (26170)Instructions burned: 5 (million) 0.16/0.36 % (26170)------------------------------ 0.16/0.36 % (26170)------------------------------ 0.16/0.36 % (26166)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_26058 for (1799ds/183Mi) 0.16/0.37 % (26167)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_26058 for (1799ds/4Mi) 0.16/0.37 % (26169)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_26058 for (1799ds/2Mi) 0.16/0.37 % (26171)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_26058 for (1799ds/275Mi) 0.16/0.37 % (26169)Instruction limit reached! 0.16/0.37 % (26169)------------------------------ 0.16/0.37 % (26169)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.37 % (26169)Termination reason: Unknown 0.16/0.37 % (26169)Termination phase: shuffling 0.16/0.37 0.16/0.37 % (26169)Memory used [KB]: 1279 0.16/0.37 % (26169)Time elapsed: 0.003 s 0.16/0.37 % (26169)Instructions burned: 3 (million) 0.16/0.37 % (26169)------------------------------ 0.16/0.37 % (26169)------------------------------ 0.16/0.37 % (26167)Instruction limit reached! 0.16/0.37 % (26167)------------------------------ 0.16/0.37 % (26167)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.37 % (26167)Termination reason: Unknown 0.16/0.37 % (26167)Termination phase: shuffling 0.16/0.37 0.16/0.37 % (26167)Memory used [KB]: 1279 0.16/0.37 % (26167)Time elapsed: 0.004 s 0.16/0.37 % (26167)Instructions burned: 5 (million) 0.16/0.37 % (26167)------------------------------ 0.16/0.37 % (26167)------------------------------ 0.16/0.37 % (26172)Instruction limit reached! 0.16/0.37 % (26172)------------------------------ 0.16/0.37 % (26172)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.37 % (26172)Termination reason: Unknown 0.16/0.37 % (26172)Termination phase: Property scanning 0.16/0.37 0.16/0.37 % (26172)Memory used [KB]: 1663 0.16/0.37 % (26172)Time elapsed: 0.008 s 0.16/0.37 % (26172)Instructions burned: 18 (million) 0.16/0.37 % (26172)------------------------------ 0.16/0.37 % (26172)------------------------------ 0.16/0.37 % (26168)Instruction limit reached! 0.16/0.37 % (26168)------------------------------ 0.16/0.37 % (26168)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.37 % (26168)Termination reason: Unknown 0.16/0.37 % (26168)Termination phase: Property scanning 0.16/0.37 0.16/0.37 % (26168)Memory used [KB]: 1791 0.16/0.37 % (26168)Time elapsed: 0.010 s 0.16/0.37 % (26168)Instructions burned: 27 (million) 0.16/0.37 % (26168)------------------------------ 0.16/0.37 % (26168)------------------------------ 0.16/0.37 % (26173)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_26058 for (1799ds/3Mi) 0.16/0.37 % (26173)Instruction limit reached! 0.16/0.37 % (26173)------------------------------ 0.16/0.37 % (26173)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.37 % (26173)Termination reason: Unknown 0.16/0.37 % (26173)Termination phase: shuffling 0.16/0.37 0.16/0.37 % (26173)Memory used [KB]: 1279 0.16/0.37 % (26173)Time elapsed: 0.003 s 0.16/0.37 % (26173)Instructions burned: 4 (million) 0.16/0.37 % (26173)------------------------------ 0.16/0.37 % (26173)------------------------------ 0.16/0.38 % (26176)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_26058 for (1799ds/3Mi) 0.16/0.38 % (26177)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_26058 for (1799ds/1041Mi) 0.16/0.38 % (26171)Refutation not found, incomplete strategy 0.16/0.38 % (26171)------------------------------ 0.16/0.38 % (26171)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.38 % (26171)Termination reason: Refutation not found, incomplete strategy 0.16/0.38 0.16/0.38 0.16/0.38 % (26171)Memory used [KB]: 6140 0.16/0.38 % (26171)Time elapsed: 0.014 s 0.16/0.38 % (26171)Instructions burned: 24 (million) 0.16/0.38 % (26171)------------------------------ 0.16/0.38 % (26171)------------------------------ 0.16/0.38 % (26176)Instruction limit reached! 0.16/0.38 % (26176)------------------------------ 0.16/0.38 % (26176)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.38 % (26176)Termination reason: Unknown 0.16/0.38 % (26176)Termination phase: shuffling 0.16/0.38 0.16/0.38 % (26176)Memory used [KB]: 1279 0.16/0.38 % (26176)Time elapsed: 0.003 s 0.16/0.38 % (26176)Instructions burned: 5 (million) 0.16/0.38 % (26176)------------------------------ 0.16/0.38 % (26176)------------------------------ 0.16/0.38 % (26174)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_26058 for (1799ds/37Mi) 0.16/0.38 % (26175)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_26058 for (1799ds/15Mi) 0.16/0.38 % (26178)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_26058 for (1799ds/7Mi) 0.16/0.38 % (26178)Instruction limit reached! 0.16/0.38 % (26178)------------------------------ 0.16/0.38 % (26178)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.38 % (26178)Termination reason: Unknown 0.16/0.38 % (26178)Termination phase: shuffling 0.16/0.38 0.16/0.38 % (26178)Memory used [KB]: 1407 0.16/0.38 % (26178)Time elapsed: 0.004 s 0.16/0.38 % (26178)Instructions burned: 7 (million) 0.16/0.38 % (26178)------------------------------ 0.16/0.38 % (26178)------------------------------ 0.16/0.39 % (26180)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_26058 for (1799ds/3Mi) 0.16/0.39 % (26175)Instruction limit reached! 0.16/0.39 % (26175)------------------------------ 0.16/0.39 % (26175)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.39 % (26175)Termination reason: Unknown 0.16/0.39 % (26175)Termination phase: Property scanning 0.16/0.39 0.16/0.39 % (26175)Memory used [KB]: 1663 0.16/0.39 % (26175)Time elapsed: 0.010 s 0.16/0.39 % (26175)Instructions burned: 15 (million) 0.16/0.39 % (26175)------------------------------ 0.16/0.39 % (26175)------------------------------ 0.16/0.39 % (26180)Instruction limit reached! 0.16/0.39 % (26180)------------------------------ 0.16/0.39 % (26180)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.39 % (26180)Termination reason: Unknown 0.16/0.39 % (26180)Termination phase: shuffling 0.16/0.39 0.16/0.39 % (26180)Memory used [KB]: 1279 0.16/0.39 % (26180)Time elapsed: 0.003 s 0.16/0.39 % (26180)Instructions burned: 4 (million) 0.16/0.39 % (26180)------------------------------ 0.16/0.39 % (26180)------------------------------ 0.16/0.39 % (26179)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_26058 for (1799ds/16Mi) 0.16/0.39 % (26181)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_26058 for (1799ds/3Mi) 0.16/0.39 % (26174)Instruction limit reached! 0.16/0.39 % (26174)------------------------------ 0.16/0.39 % (26174)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.39 % (26174)Termination reason: Unknown 0.16/0.39 % (26174)Termination phase: Property scanning 0.16/0.39 0.16/0.39 % (26174)Memory used [KB]: 1791 0.16/0.39 % (26174)Time elapsed: 0.015 s 0.16/0.39 % (26174)Instructions burned: 39 (million) 0.16/0.39 % (26174)------------------------------ 0.16/0.39 % (26174)------------------------------ 0.16/0.39 % (26181)Instruction limit reached! 0.16/0.39 % (26181)------------------------------ 0.16/0.39 % (26181)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.39 % (26181)Termination reason: Unknown 0.16/0.39 % (26181)Termination phase: shuffling 0.16/0.39 0.16/0.39 % (26181)Memory used [KB]: 1279 0.16/0.39 % (26181)Time elapsed: 0.003 s 0.16/0.39 % (26181)Instructions burned: 4 (million) 0.16/0.39 % (26181)------------------------------ 0.16/0.39 % (26181)------------------------------ 0.16/0.40 % (26179)Instruction limit reached! 0.16/0.40 % (26179)------------------------------ 0.16/0.40 % (26179)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.40 % (26179)Termination reason: Unknown 0.16/0.40 % (26179)Termination phase: shuffling 0.16/0.40 0.16/0.40 % (26179)Memory used [KB]: 1663 0.16/0.40 % (26179)Time elapsed: 0.008 s 0.16/0.40 % (26179)Instructions burned: 17 (million) 0.16/0.40 % (26179)------------------------------ 0.16/0.40 % (26179)------------------------------ 0.16/0.40 % (26183)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_26058 for (1799ds/3Mi) 0.16/0.40 % (26183)Instruction limit reached! 0.16/0.40 % (26183)------------------------------ 0.16/0.40 % (26183)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.16/0.40 % (26183)Termination reason: Unknown 0.16/0.40 % (26183)Termination phase: shuffling 0.16/0.40 0.16/0.40 % (26183)Memory used [KB]: 1279 0.16/0.40 % (26183)Time elapsed: 0.003 s 0.16/0.40 % (26183)Instructions burned: 4 (million) 0.16/0.40 % (26183)------------------------------ 0.16/0.40 % (26183)------------------------------ 0.16/0.40 % (26166)First to succeed. 0.16/0.40 % (26182)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_26058 for (1799ds/7Mi) 0.20/0.40 % (26185)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_26058 for (1799ds/18Mi) 0.20/0.40 % (26184)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_26058 for (1799ds/4Mi) 0.20/0.41 % (26182)Instruction limit reached! 0.20/0.41 % (26182)------------------------------ 0.20/0.41 % (26182)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.41 % (26182)Termination reason: Unknown 0.20/0.41 % (26182)Termination phase: shuffling 0.20/0.41 0.20/0.41 % (26182)Memory used [KB]: 1407 0.20/0.41 % (26182)Time elapsed: 0.005 s 0.20/0.41 % (26182)Instructions burned: 9 (million) 0.20/0.41 % (26182)------------------------------ 0.20/0.41 % (26182)------------------------------ 0.20/0.41 % (26184)Instruction limit reached! 0.20/0.41 % (26184)------------------------------ 0.20/0.41 % (26184)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.41 % (26184)Termination reason: Unknown 0.20/0.41 % (26184)Termination phase: shuffling 0.20/0.41 0.20/0.41 % (26184)Memory used [KB]: 1279 0.20/0.41 % (26184)Time elapsed: 0.004 s 0.20/0.41 % (26184)Instructions burned: 6 (million) 0.20/0.41 % (26184)------------------------------ 0.20/0.41 % (26184)------------------------------ 0.20/0.41 % (26166)Refutation found. Thanks to Tanya! 0.20/0.41 % SZS status Theorem for E---3.1_26058 0.20/0.41 % SZS output start Proof for E---3.1_26058 0.20/0.41 thf(type_def_5, type, term: $tType). 0.20/0.41 thf(type_def_7, type, subst: $tType). 0.20/0.41 thf(func_def_0, type, term: $tType). 0.20/0.41 thf(func_def_1, type, subst: $tType). 0.20/0.41 thf(func_def_2, type, one: term). 0.20/0.41 thf(func_def_3, type, ap: term > term > term). 0.20/0.41 thf(func_def_4, type, lam: term > term). 0.20/0.41 thf(func_def_5, type, sub: term > subst > term). 0.20/0.41 thf(func_def_6, type, id: subst). 0.20/0.41 thf(func_def_7, type, sh: subst). 0.20/0.41 thf(func_def_8, type, push: term > subst > subst). 0.20/0.41 thf(func_def_9, type, comp: subst > subst > subst). 0.20/0.41 thf(func_def_10, type, var: term > $o). 0.20/0.41 thf(func_def_18, type, hoasap: subst > term > subst > term > term). 0.20/0.41 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term). 0.20/0.41 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o). 0.20/0.41 thf(func_def_107, type, hoasvar: subst > term > subst > $o). 0.20/0.41 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o). 0.20/0.41 thf(func_def_142, type, sK1: subst > term > term). 0.20/0.41 thf(func_def_143, type, sK2: subst > term > term). 0.20/0.41 thf(func_def_144, type, sK3: term). 0.20/0.41 thf(func_def_145, type, sK4: subst). 0.20/0.41 thf(f660,plain,( 0.20/0.41 $false), 0.20/0.41 inference(trivial_inequality_removal,[],[f659])). 0.20/0.41 thf(f659,plain,( 0.20/0.41 ((sK1 @ sK4 @ sK3) != (sK1 @ sK4 @ sK3))), 0.20/0.41 inference(superposition,[],[f576,f626])). 0.20/0.41 thf(f626,plain,( 0.20/0.41 ( ! [X0 : term,X1 : subst] : (((sK2 @ X1 @ X0) = (sK1 @ X1 @ X0))) )), 0.20/0.41 inference(superposition,[],[f586,f614])). 0.20/0.41 thf(f614,plain,( 0.20/0.41 ( ! [X0 : term,X1 : subst] : (((sK2 @ X1 @ X0) = (sub @ (sK1 @ sh @ one) @ (push @ X0 @ X1)))) )), 0.20/0.41 inference(superposition,[],[f610,f581])). 0.20/0.41 thf(f581,plain,( 0.20/0.41 ((sK1 @ sh @ one) = (sK2 @ sh @ one))), 0.20/0.41 inference(equality_resolution,[],[f579])). 0.20/0.41 thf(f579,plain,( 0.20/0.41 ( ! [X0 : term] : (((lam @ X0) != (lam @ (sK1 @ sh @ one))) | ((sK2 @ sh @ one) = X0)) )), 0.20/0.41 inference(superposition,[],[f546,f571])). 0.20/0.41 thf(f571,plain,( 0.20/0.41 ((lam @ (sK2 @ sh @ one)) = (lam @ (sK1 @ sh @ one)))), 0.20/0.41 inference(equality_proxy_clausification,[],[f570])). 0.20/0.41 thf(f570,plain,( 0.20/0.41 ($true = ((lam @ (sK2 @ sh @ one)) = (lam @ (sK1 @ sh @ one))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f560])). 0.20/0.41 thf(f560,plain,( 0.20/0.41 ((((lam @ (sK2 @ sh @ one)) = (lam @ (sK1 @ sh @ one))) => (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sK2 @ Y1 @ Y0) = (sK1 @ Y1 @ Y0))))))) = $false)), 0.20/0.41 inference(binary_proxy_clausification,[],[f559])). 0.20/0.41 thf(f559,plain,( 0.20/0.41 ($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK2 @ Y1 @ Y0) @ Y2) = (sK2 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))) => (((lam @ (sK2 @ sh @ one)) = (lam @ (sK1 @ sh @ one))) => (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sK2 @ Y1 @ Y0) = (sK1 @ Y1 @ Y0)))))))))), 0.20/0.41 inference(beta_eta_normalization,[],[f558])). 0.20/0.41 thf(f558,plain,( 0.20/0.41 ($false = ((^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (((lam @ (Y0 @ sh @ one)) = (lam @ (sK1 @ sh @ one))) => (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((Y0 @ Y2 @ Y1) = (sK1 @ Y2 @ Y1))))))))) @ sK2))), 0.20/0.41 inference(sigma_clausification,[],[f549])). 0.20/0.41 thf(f549,plain,( 0.20/0.41 ($false = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (((lam @ (Y0 @ sh @ one)) = (lam @ (sK1 @ sh @ one))) => (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((Y0 @ Y2 @ Y1) = (sK1 @ Y2 @ Y1)))))))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f548])). 0.20/0.41 thf(f548,plain,( 0.20/0.41 (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2))))))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (((lam @ (Y0 @ sh @ one)) = (lam @ (sK1 @ sh @ one))) => (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((Y0 @ Y2 @ Y1) = (sK1 @ Y2 @ Y1))))))))))) = $false)), 0.20/0.41 inference(beta_eta_normalization,[],[f547])). 0.20/0.41 thf(f547,plain,( 0.20/0.41 ($false = ((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => (((lam @ (Y1 @ sh @ one)) = (lam @ (Y0 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2)))))))))))) @ sK1))), 0.20/0.41 inference(sigma_clausification,[],[f538])). 0.20/0.41 thf(f538,plain,( 0.20/0.41 ($false = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => (((lam @ (Y1 @ sh @ one)) = (lam @ (Y0 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2))))))))))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f531])). 0.20/0.41 thf(f531,plain,( 0.20/0.41 (((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => (((lam @ (Y1 @ sh @ one)) = (lam @ (Y0 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2)))))))))))))) = $false)), 0.20/0.41 inference(binary_proxy_clausification,[],[f524])). 0.20/0.41 thf(f524,plain,( 0.20/0.41 ($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((comp @ sh @ (push @ Y0 @ Y1)) = Y1))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => (((lam @ (Y1 @ sh @ one)) = (lam @ (Y0 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2))))))))))))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f523])). 0.20/0.41 thf(f523,plain,( 0.20/0.41 ($true != ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ one @ (push @ Y0 @ Y1)) = Y0))))) => ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((comp @ sh @ (push @ Y0 @ Y1)) = Y1))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => (((lam @ (Y1 @ sh @ one)) = (lam @ (Y0 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2)))))))))))))))))), 0.20/0.41 inference(beta_eta_normalization,[],[f522])). 0.20/0.41 thf(f522,plain,( 0.20/0.41 ($true != ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ one @ (push @ Y0 @ Y1)) = Y0))))) => ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((comp @ sh @ (push @ Y0 @ Y1)) = Y1))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2)))))))))))))))))), 0.20/0.41 inference(definition_unfolding,[],[f416,f497])). 0.20/0.41 thf(f497,plain,( 0.20/0.41 (hoaslaminj_lthm = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ one @ (push @ Y0 @ Y1)) = Y0))))) => ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((comp @ sh @ (push @ Y0 @ Y1)) = Y1))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2)))))))))))))))))), 0.20/0.41 inference(definition_unfolding,[],[f362,f391,f388,f424,f452])). 0.20/0.41 thf(f452,plain,( 0.20/0.41 (hoaslaminj = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2))))))))))))))), 0.20/0.41 inference(definition_unfolding,[],[f339,f427,f427])). 0.20/0.41 thf(f427,plain,( 0.20/0.41 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (lam @ (Y1 @ sh @ one))))))), 0.20/0.41 inference(cnf_transformation,[],[f201])). 0.20/0.41 thf(f201,plain,( 0.20/0.41 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (lam @ (Y1 @ sh @ one))))))), 0.20/0.41 inference(fool_elimination,[],[f200])). 0.20/0.41 thf(f200,plain,( 0.20/0.41 ((^[X0 : subst, X1 : subst > term > term] : (lam @ (X1 @ sh @ one))) = hoaslam)), 0.20/0.41 inference(rectify,[],[f56])). 0.20/0.41 thf(f56,axiom,( 0.20/0.41 ((^[X2 : subst, X10 : subst > term > term] : (lam @ (X10 @ sh @ one))) = hoaslam)), 0.20/0.41 file('/export/starexec/sandbox/tmp/tmp.v8xjebNtRA/E---3.1_26058.p',hoaslam)). 0.20/0.41 thf(f339,plain,( 0.20/0.41 (hoaslaminj = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => (((hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2))))))))))))))), 0.20/0.41 inference(cnf_transformation,[],[f223])). 0.20/0.41 thf(f223,plain,( 0.20/0.41 (hoaslaminj = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => (((hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y1 @ Y3 @ Y2) = (Y0 @ Y3 @ Y2))))))))))))))), 0.20/0.41 inference(fool_elimination,[],[f222])). 0.20/0.41 thf(f222,plain,( 0.20/0.41 (hoaslaminj = ! [X0 : subst > term > term] : (! [X1 : subst,X2 : term,X3 : subst] : ((sub @ (X0 @ X3 @ X2) @ X1) = (X0 @ (comp @ X3 @ X1) @ (sub @ X2 @ X1))) => ! [X4 : subst > term > term] : (! [X5 : subst,X6 : subst,X7 : term] : ((sub @ (X4 @ X6 @ X7) @ X5) = (X4 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5))) => (((hoaslam @ id @ (^[X8 : subst, X9 : term] : (X4 @ X8 @ X9))) = (hoaslam @ id @ (^[X10 : subst, X11 : term] : (X0 @ X10 @ X11)))) => ! [X12 : subst,X13 : term] : ((X4 @ X12 @ X13) = (X0 @ X12 @ X13))))))), 0.20/0.41 inference(rectify,[],[f64])). 0.20/0.41 thf(f64,axiom,( 0.20/0.41 (hoaslaminj = ! [X10 : subst > term > term] : (! [X3 : subst,X0 : term,X2 : subst] : ((sub @ (X10 @ X2 @ X0) @ X3) = (X10 @ (comp @ X2 @ X3) @ (sub @ X0 @ X3))) => ! [X11 : subst > term > term] : (! [X3 : subst,X2 : subst,X0 : term] : ((sub @ (X11 @ X2 @ X0) @ X3) = (X11 @ (comp @ X2 @ X3) @ (sub @ X0 @ X3))) => (((hoaslam @ id @ (^[X2 : subst, X0 : term] : (X11 @ X2 @ X0))) = (hoaslam @ id @ (^[X2 : subst, X0 : term] : (X10 @ X2 @ X0)))) => ! [X2 : subst,X0 : term] : ((X10 @ X2 @ X0) = (X11 @ X2 @ X0))))))), 0.20/0.41 file('/export/starexec/sandbox/tmp/tmp.v8xjebNtRA/E---3.1_26058.p',hoaslaminj)). 0.20/0.41 thf(f424,plain,( 0.20/0.41 (laminj = (!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))))), 0.20/0.41 inference(cnf_transformation,[],[f128])). 0.20/0.41 thf(f128,plain,( 0.20/0.41 (laminj = (!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))))), 0.20/0.41 inference(fool_elimination,[],[f127])). 0.20/0.41 thf(f127,plain,( 0.20/0.41 (laminj = ! [X0 : term,X1 : term] : (((lam @ X0) = (lam @ X1)) => (X0 = X1)))), 0.20/0.41 inference(rectify,[],[f18])). 0.20/0.41 thf(f18,axiom,( 0.20/0.41 (laminj = ! [X1 : term,X0 : term] : (((lam @ X0) = (lam @ X1)) => (X0 = X1)))), 0.20/0.41 file('/export/starexec/sandbox/tmp/tmp.v8xjebNtRA/E---3.1_26058.p',laminj)). 0.20/0.41 thf(f388,plain,( 0.20/0.41 (axshiftcons = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((comp @ sh @ (push @ Y0 @ Y1)) = Y1))))))), 0.20/0.41 inference(cnf_transformation,[],[f307])). 0.20/0.41 thf(f307,plain,( 0.20/0.41 (axshiftcons = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((comp @ sh @ (push @ Y0 @ Y1)) = Y1))))))), 0.20/0.41 inference(fool_elimination,[],[f306])). 0.20/0.41 thf(f306,plain,( 0.20/0.41 (axshiftcons = ! [X0 : subst,X1 : term] : ((comp @ sh @ (push @ X1 @ X0)) = X0))), 0.20/0.41 inference(rectify,[],[f7])). 0.20/0.41 thf(f7,axiom,( 0.20/0.41 (axshiftcons = ! [X2 : subst,X0 : term] : ((comp @ sh @ (push @ X0 @ X2)) = X2))), 0.20/0.41 file('/export/starexec/sandbox/tmp/tmp.v8xjebNtRA/E---3.1_26058.p',axshiftcons)). 0.20/0.41 thf(f391,plain,( 0.20/0.41 (axvarcons = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ one @ (push @ Y0 @ Y1)) = Y0))))))), 0.20/0.41 inference(cnf_transformation,[],[f285])). 0.20/0.41 thf(f285,plain,( 0.20/0.41 (axvarcons = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ one @ (push @ Y0 @ Y1)) = Y0))))))), 0.20/0.41 inference(fool_elimination,[],[f284])). 0.20/0.41 thf(f284,plain,( 0.20/0.41 (axvarcons = ! [X0 : subst,X1 : term] : ((sub @ one @ (push @ X1 @ X0)) = X1))), 0.20/0.41 inference(rectify,[],[f2])). 0.20/0.41 thf(f2,axiom,( 0.20/0.41 (axvarcons = ! [X2 : subst,X0 : term] : ((sub @ one @ (push @ X0 @ X2)) = X0))), 0.20/0.41 file('/export/starexec/sandbox/tmp/tmp.v8xjebNtRA/E---3.1_26058.p',axvarcons)). 0.20/0.41 thf(f362,plain,( 0.20/0.41 (hoaslaminj_lthm = (axvarcons => (axshiftcons => (laminj => hoaslaminj))))), 0.20/0.41 inference(cnf_transformation,[],[f219])). 0.20/0.41 thf(f219,plain,( 0.20/0.41 (hoaslaminj_lthm = (axvarcons => (axshiftcons => (laminj => hoaslaminj))))), 0.20/0.41 inference(fool_elimination,[],[f218])). 0.20/0.41 thf(f218,plain,( 0.20/0.41 (hoaslaminj_lthm = axvarcons => (axshiftcons => (laminj => hoaslaminj)))), 0.20/0.41 inference(rectify,[],[f66])). 0.20/0.41 thf(f66,axiom,( 0.20/0.41 (hoaslaminj_lthm = axvarcons => (axshiftcons => (laminj => hoaslaminj)))), 0.20/0.41 file('/export/starexec/sandbox/tmp/tmp.v8xjebNtRA/E---3.1_26058.p',hoaslaminj_lthm)). 0.20/0.41 thf(f416,plain,( 0.20/0.41 (hoaslaminj_lthm != $true)), 0.20/0.41 inference(cnf_transformation,[],[f330])). 0.20/0.41 thf(f330,plain,( 0.20/0.41 (hoaslaminj_lthm != $true)), 0.20/0.41 inference(flattening,[],[f257])). 0.20/0.41 thf(f257,plain,( 0.20/0.41 ~(hoaslaminj_lthm = $true)), 0.20/0.41 inference(fool_elimination,[],[f256])). 0.20/0.41 thf(f256,plain,( 0.20/0.41 ~hoaslaminj_lthm), 0.20/0.41 inference(rectify,[],[f115])). 0.20/0.41 thf(f115,negated_conjecture,( 0.20/0.41 ~hoaslaminj_lthm), 0.20/0.41 inference(negated_conjecture,[],[f114])). 0.20/0.41 thf(f114,conjecture,( 0.20/0.41 hoaslaminj_lthm), 0.20/0.41 file('/export/starexec/sandbox/tmp/tmp.v8xjebNtRA/E---3.1_26058.p',thm)). 0.20/0.41 thf(f546,plain,( 0.20/0.41 ( ! [X2 : term,X1 : term] : (((lam @ X1) != (lam @ X2)) | (X1 = X2)) )), 0.20/0.41 inference(equality_proxy_clausification,[],[f545])). 0.20/0.41 thf(f545,plain,( 0.20/0.41 ( ! [X2 : term,X1 : term] : (($false = ((lam @ X2) = (lam @ X1))) | (X1 = X2)) )), 0.20/0.41 inference(equality_proxy_clausification,[],[f544])). 0.20/0.41 thf(f544,plain,( 0.20/0.41 ( ! [X2 : term,X1 : term] : (($true = (X2 = X1)) | ($false = ((lam @ X2) = (lam @ X1)))) )), 0.20/0.41 inference(binary_proxy_clausification,[],[f543])). 0.20/0.41 thf(f543,plain,( 0.20/0.41 ( ! [X2 : term,X1 : term] : (($true = (((lam @ X2) = (lam @ X1)) => (X2 = X1)))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f542])). 0.20/0.41 thf(f542,plain,( 0.20/0.41 ( ! [X2 : term,X1 : term] : (($true = ((^[Y0 : term]: (((lam @ Y0) = (lam @ X1)) => (Y0 = X1))) @ X2))) )), 0.20/0.41 inference(pi_clausification,[],[f541])). 0.20/0.41 thf(f541,plain,( 0.20/0.41 ( ! [X1 : term] : (($true = (!! @ term @ (^[Y0 : term]: (((lam @ Y0) = (lam @ X1)) => (Y0 = X1)))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f540])). 0.20/0.41 thf(f540,plain,( 0.20/0.41 ( ! [X1 : term] : (($true = ((^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0))))) @ X1))) )), 0.20/0.41 inference(pi_clausification,[],[f539])). 0.20/0.41 thf(f539,plain,( 0.20/0.41 ($true = (!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f531])). 0.20/0.41 thf(f610,plain,( 0.20/0.41 ( ! [X0 : term,X1 : subst] : (((sub @ (sK2 @ sh @ one) @ (push @ X0 @ X1)) = (sK2 @ X1 @ X0))) )), 0.20/0.41 inference(superposition,[],[f584,f537])). 0.20/0.41 thf(f537,plain,( 0.20/0.41 ( ! [X2 : subst,X1 : term] : (((comp @ sh @ (push @ X1 @ X2)) = X2)) )), 0.20/0.41 inference(equality_proxy_clausification,[],[f536])). 0.20/0.41 thf(f536,plain,( 0.20/0.41 ( ! [X2 : subst,X1 : term] : (($true = ((comp @ sh @ (push @ X1 @ X2)) = X2))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f535])). 0.20/0.41 thf(f535,plain,( 0.20/0.41 ( ! [X2 : subst,X1 : term] : (($true = ((^[Y0 : subst]: ((comp @ sh @ (push @ X1 @ Y0)) = Y0)) @ X2))) )), 0.20/0.41 inference(pi_clausification,[],[f534])). 0.20/0.41 thf(f534,plain,( 0.20/0.41 ( ! [X1 : term] : (($true = (!! @ subst @ (^[Y0 : subst]: ((comp @ sh @ (push @ X1 @ Y0)) = Y0))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f533])). 0.20/0.41 thf(f533,plain,( 0.20/0.41 ( ! [X1 : term] : (($true = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((comp @ sh @ (push @ Y0 @ Y1)) = Y1)))) @ X1))) )), 0.20/0.41 inference(pi_clausification,[],[f532])). 0.20/0.41 thf(f532,plain,( 0.20/0.41 ($true = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((comp @ sh @ (push @ Y0 @ Y1)) = Y1))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f524])). 0.20/0.41 thf(f584,plain,( 0.20/0.41 ( ! [X2 : subst,X0 : term,X1 : subst] : (((sub @ (sK2 @ X2 @ one) @ (push @ X0 @ X1)) = (sK2 @ (comp @ X2 @ (push @ X0 @ X1)) @ X0))) )), 0.20/0.41 inference(superposition,[],[f568,f530])). 0.20/0.41 thf(f530,plain,( 0.20/0.41 ( ! [X2 : subst,X1 : term] : (((sub @ one @ (push @ X1 @ X2)) = X1)) )), 0.20/0.41 inference(equality_proxy_clausification,[],[f529])). 0.20/0.41 thf(f529,plain,( 0.20/0.41 ( ! [X2 : subst,X1 : term] : (($true = ((sub @ one @ (push @ X1 @ X2)) = X1))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f528])). 0.20/0.41 thf(f528,plain,( 0.20/0.41 ( ! [X2 : subst,X1 : term] : (($true = ((^[Y0 : subst]: ((sub @ one @ (push @ X1 @ Y0)) = X1)) @ X2))) )), 0.20/0.41 inference(pi_clausification,[],[f527])). 0.20/0.41 thf(f527,plain,( 0.20/0.41 ( ! [X1 : term] : (($true = (!! @ subst @ (^[Y0 : subst]: ((sub @ one @ (push @ X1 @ Y0)) = X1))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f526])). 0.20/0.41 thf(f526,plain,( 0.20/0.41 ( ! [X1 : term] : (($true = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ one @ (push @ Y0 @ Y1)) = Y0)))) @ X1))) )), 0.20/0.41 inference(pi_clausification,[],[f525])). 0.20/0.41 thf(f525,plain,( 0.20/0.41 ($true = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ one @ (push @ Y0 @ Y1)) = Y0))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f523])). 0.20/0.41 thf(f568,plain,( 0.20/0.41 ( ! [X2 : subst,X3 : subst,X1 : term] : (((sK2 @ (comp @ X2 @ X3) @ (sub @ X1 @ X3)) = (sub @ (sK2 @ X2 @ X1) @ X3))) )), 0.20/0.41 inference(equality_proxy_clausification,[],[f567])). 0.20/0.41 thf(f567,plain,( 0.20/0.41 ( ! [X2 : subst,X3 : subst,X1 : term] : (($true = ((sub @ (sK2 @ X2 @ X1) @ X3) = (sK2 @ (comp @ X2 @ X3) @ (sub @ X1 @ X3))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f566])). 0.20/0.41 thf(f566,plain,( 0.20/0.41 ( ! [X2 : subst,X3 : subst,X1 : term] : (($true = ((^[Y0 : subst]: ((sub @ (sK2 @ X2 @ X1) @ Y0) = (sK2 @ (comp @ X2 @ Y0) @ (sub @ X1 @ Y0)))) @ X3))) )), 0.20/0.41 inference(pi_clausification,[],[f565])). 0.20/0.41 thf(f565,plain,( 0.20/0.41 ( ! [X2 : subst,X1 : term] : (($true = (!! @ subst @ (^[Y0 : subst]: ((sub @ (sK2 @ X2 @ X1) @ Y0) = (sK2 @ (comp @ X2 @ Y0) @ (sub @ X1 @ Y0))))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f564])). 0.20/0.41 thf(f564,plain,( 0.20/0.41 ( ! [X2 : subst,X1 : term] : (($true = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK2 @ Y0 @ X1) @ Y1) = (sK2 @ (comp @ Y0 @ Y1) @ (sub @ X1 @ Y1)))))) @ X2))) )), 0.20/0.41 inference(pi_clausification,[],[f563])). 0.20/0.41 thf(f563,plain,( 0.20/0.41 ( ! [X1 : term] : (($true = (!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK2 @ Y0 @ X1) @ Y1) = (sK2 @ (comp @ Y0 @ Y1) @ (sub @ X1 @ Y1))))))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f562])). 0.20/0.41 thf(f562,plain,( 0.20/0.41 ( ! [X1 : term] : (($true = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK2 @ Y1 @ Y0) @ Y2) = (sK2 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)))))))) @ X1))) )), 0.20/0.41 inference(pi_clausification,[],[f561])). 0.20/0.41 thf(f561,plain,( 0.20/0.41 ($true = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK2 @ Y1 @ Y0) @ Y2) = (sK2 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f559])). 0.20/0.41 thf(f586,plain,( 0.20/0.41 ( ! [X0 : term,X1 : subst] : (((sK1 @ X1 @ X0) = (sub @ (sK1 @ sh @ one) @ (push @ X0 @ X1)))) )), 0.20/0.41 inference(superposition,[],[f582,f537])). 0.20/0.41 thf(f582,plain,( 0.20/0.41 ( ! [X2 : subst,X0 : term,X1 : subst] : (((sub @ (sK1 @ X2 @ one) @ (push @ X0 @ X1)) = (sK1 @ (comp @ X2 @ (push @ X0 @ X1)) @ X0))) )), 0.20/0.41 inference(superposition,[],[f557,f530])). 0.20/0.41 thf(f557,plain,( 0.20/0.41 ( ! [X2 : term,X3 : subst,X1 : subst] : (((sub @ (sK1 @ X1 @ X2) @ X3) = (sK1 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) )), 0.20/0.41 inference(equality_proxy_clausification,[],[f556])). 0.20/0.41 thf(f556,plain,( 0.20/0.41 ( ! [X2 : term,X3 : subst,X1 : subst] : (($true = ((sub @ (sK1 @ X1 @ X2) @ X3) = (sK1 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f555])). 0.20/0.41 thf(f555,plain,( 0.20/0.41 ( ! [X2 : term,X3 : subst,X1 : subst] : (($true = ((^[Y0 : subst]: ((sub @ (sK1 @ X1 @ X2) @ Y0) = (sK1 @ (comp @ X1 @ Y0) @ (sub @ X2 @ Y0)))) @ X3))) )), 0.20/0.41 inference(pi_clausification,[],[f554])). 0.20/0.41 thf(f554,plain,( 0.20/0.41 ( ! [X2 : term,X1 : subst] : (($true = (!! @ subst @ (^[Y0 : subst]: ((sub @ (sK1 @ X1 @ X2) @ Y0) = (sK1 @ (comp @ X1 @ Y0) @ (sub @ X2 @ Y0))))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f553])). 0.20/0.41 thf(f553,plain,( 0.20/0.41 ( ! [X2 : term,X1 : subst] : (($true = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK1 @ X1 @ Y0) @ Y1) = (sK1 @ (comp @ X1 @ Y1) @ (sub @ Y0 @ Y1)))))) @ X2))) )), 0.20/0.41 inference(pi_clausification,[],[f552])). 0.20/0.41 thf(f552,plain,( 0.20/0.41 ( ! [X1 : subst] : (($true = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK1 @ X1 @ Y0) @ Y1) = (sK1 @ (comp @ X1 @ Y1) @ (sub @ Y0 @ Y1))))))))) )), 0.20/0.41 inference(beta_eta_normalization,[],[f551])). 0.20/0.41 thf(f551,plain,( 0.20/0.41 ( ! [X1 : subst] : (($true = ((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)))))))) @ X1))) )), 0.20/0.41 inference(pi_clausification,[],[f550])). 0.20/0.41 thf(f550,plain,( 0.20/0.41 ($true = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2))))))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f548])). 0.20/0.41 thf(f576,plain,( 0.20/0.41 ((sK1 @ sK4 @ sK3) != (sK2 @ sK4 @ sK3))), 0.20/0.41 inference(equality_proxy_clausification,[],[f575])). 0.20/0.41 thf(f575,plain,( 0.20/0.41 (((sK2 @ sK4 @ sK3) = (sK1 @ sK4 @ sK3)) = $false)), 0.20/0.41 inference(beta_eta_normalization,[],[f574])). 0.20/0.41 thf(f574,plain,( 0.20/0.41 (((^[Y0 : subst]: ((sK2 @ Y0 @ sK3) = (sK1 @ Y0 @ sK3))) @ sK4) = $false)), 0.20/0.41 inference(sigma_clausification,[],[f573])). 0.20/0.41 thf(f573,plain,( 0.20/0.41 ((!! @ subst @ (^[Y0 : subst]: ((sK2 @ Y0 @ sK3) = (sK1 @ Y0 @ sK3)))) = $false)), 0.20/0.41 inference(beta_eta_normalization,[],[f572])). 0.20/0.41 thf(f572,plain,( 0.20/0.41 (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sK2 @ Y1 @ Y0) = (sK1 @ Y1 @ Y0))))) @ sK3) = $false)), 0.20/0.41 inference(sigma_clausification,[],[f569])). 0.20/0.41 thf(f569,plain,( 0.20/0.41 ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sK2 @ Y1 @ Y0) = (sK1 @ Y1 @ Y0)))))))), 0.20/0.41 inference(binary_proxy_clausification,[],[f560])). 0.20/0.41 % SZS output end Proof for E---3.1_26058 0.20/0.41 % (26166)------------------------------ 0.20/0.41 % (26166)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.41 % (26166)Termination reason: Refutation 0.20/0.41 0.20/0.41 % (26166)Memory used [KB]: 6908 0.20/0.41 % (26166)Time elapsed: 0.045 s 0.20/0.41 % (26166)Instructions burned: 112 (million) 0.20/0.41 % (26166)------------------------------ 0.20/0.41 % (26166)------------------------------ 0.20/0.41 % (26165)Success in time 0.045 s 0.20/0.41 EOF