0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.18/0.45 % Computer : n004.cluster.edu 0.18/0.45 % Model : x86_64 x86_64 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.45 % Memory : 8046.5625MB 0.18/0.45 % OS : Linux 6.8.0-71-generic 0.18/0.45 % CPULimit : 1440 0.18/0.45 % WCLimit : 180 0.18/0.45 % DateTime : Mon Jul 27 10:30:54 UTC 2026 0.18/0.46 % CPUTime : 0.18/0.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.23/0.52 Running first-order theorem proving 0.23/0.52 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p 13.46/3.11 % (2871361)Detected formulas, will run a generic FOF schedule. 13.46/3.11 % (2871367)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1783428259:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_1799 on theBenchmark for (1799ds/134677Mi) 13.46/3.11 % (2871370)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=520978494:i=119:av=off:ss=axioms_1799 on theBenchmark for (1799ds/119Mi) 13.46/3.11 % (2871366)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3640427505:i=141193_1799 on theBenchmark for (1799ds/141193Mi) 13.46/3.11 % (2871372)dis-21_1_sil=8000:lcm=predicate:random_seed=693991702:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_1799 on theBenchmark for (1799ds/129Mi) 13.46/3.11 % (2871371)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=306069354:s2a=on:i=139:gtg=position_1799 on theBenchmark for (1799ds/139Mi) 13.46/3.11 % (2871368)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2878471423:i=141695:sd=1:nm=32:gsp=on:ss=included_1799 on theBenchmark for (1799ds/141695Mi) 13.46/3.12 % (2871369)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2366300862:i=109:sd=1:ins=1:gsp=on:ss=axioms_1799 on theBenchmark for (1799ds/109Mi) 13.46/3.12 % (2871369)Refutation not found, incomplete strategy 13.46/3.12 % (2871369)------------------------------ 13.46/3.12 % (2871369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871369)CaDiCaL version: 2.1.3 13.46/3.12 % (2871369)Termination reason: Refutation not found, incomplete strategy 13.46/3.12 % (2871369)Time elapsed: 0.001 s 13.46/3.12 % (2871369)Peak memory usage: 87 MB 13.46/3.12 % (2871370)Refutation not found, incomplete strategy 13.46/3.12 % (2871370)------------------------------ 13.46/3.12 % (2871370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871370)CaDiCaL version: 2.1.3 13.46/3.12 % (2871370)Termination reason: Refutation not found, incomplete strategy 13.46/3.12 % (2871370)Time elapsed: 0.001 s 13.46/3.12 % (2871370)Peak memory usage: 87 MB 13.46/3.12 % (2871372)Instruction limit reached! 13.46/3.12 % (2871372)------------------------------ 13.46/3.12 % (2871372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871372)CaDiCaL version: 2.1.3 13.46/3.12 % (2871372)Termination reason: Instruction limit 13.46/3.12 % (2871372)Termination phase: Saturation 13.46/3.12 % (2871372)Time elapsed: 0.129 s 13.46/3.12 % (2871372)Peak memory usage: 89 MB 13.46/3.12 % (2871372)Instructions burned: 130 (million) 13.46/3.12 % (2871371)Instruction limit reached! 13.46/3.12 % (2871371)------------------------------ 13.46/3.12 % (2871371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871371)CaDiCaL version: 2.1.3 13.46/3.12 % (2871371)Termination reason: Instruction limit 13.46/3.12 % (2871371)Termination phase: Saturation 13.46/3.12 % (2871371)Time elapsed: 0.131 s 13.46/3.12 % (2871371)Peak memory usage: 89 MB 13.46/3.12 % (2871371)Instructions burned: 139 (million) 13.46/3.12 % (2871369)------------------------------ 13.46/3.12 % (2871369)------------------------------ 13.46/3.12 % (2871370)------------------------------ 13.46/3.12 % (2871370)------------------------------ 13.46/3.12 % (2871380)lrs+10_1_sil=8000:sp=occurrence:random_seed=3421894759:i=285:sd=3:ss=axioms:sgt=8_1796 on theBenchmark for (1796ds/285Mi) 13.46/3.12 % (2871381)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2383896302:i=157:sd=1:gtg=position:ss=axioms:sgt=8_1795 on theBenchmark for (1795ds/157Mi) 13.46/3.12 % (2871381)Instruction limit reached! 13.46/3.12 % (2871381)------------------------------ 13.46/3.12 % (2871381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871381)CaDiCaL version: 2.1.3 13.46/3.12 % (2871381)Termination reason: Instruction limit 13.46/3.12 % (2871381)Termination phase: Saturation 13.46/3.12 % (2871381)Time elapsed: 0.137 s 13.46/3.12 % (2871381)Peak memory usage: 89 MB 13.46/3.12 % (2871381)Instructions burned: 157 (million) 13.46/3.12 % (2871383)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1906666901:s2a=on:i=248:s2at=1.23:gtg=position_1793 on theBenchmark for (1793ds/248Mi) 13.46/3.12 % (2871382)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2695858702:i=325:sd=1:ss=axioms:sgt=32_1793 on theBenchmark for (1793ds/325Mi) 13.46/3.12 % (2871380)Instruction limit reached! 13.46/3.12 % (2871380)------------------------------ 13.46/3.12 % (2871380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871380)CaDiCaL version: 2.1.3 13.46/3.12 % (2871380)Termination reason: Instruction limit 13.46/3.12 % (2871380)Termination phase: Saturation 13.46/3.12 % (2871380)Time elapsed: 0.279 s 13.46/3.12 % (2871380)Peak memory usage: 91 MB 13.46/3.12 % (2871380)Instructions burned: 285 (million) 13.46/3.12 % (2871383)Instruction limit reached! 13.46/3.12 % (2871383)------------------------------ 13.46/3.12 % (2871383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871383)CaDiCaL version: 2.1.3 13.46/3.12 % (2871383)Termination reason: Instruction limit 13.46/3.12 % (2871383)Termination phase: Saturation 13.46/3.12 % (2871383)Time elapsed: 0.108 s 13.46/3.12 % (2871383)Peak memory usage: 88 MB 13.46/3.12 % (2871383)Instructions burned: 250 (million) 13.46/3.12 % (2871386)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3397340237:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_1791 on theBenchmark for (1791ds/294Mi) 13.46/3.12 % (2871386)Refutation not found, incomplete strategy 13.46/3.12 % (2871386)------------------------------ 13.46/3.12 % (2871386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871386)CaDiCaL version: 2.1.3 13.46/3.12 % (2871386)Termination reason: Refutation not found, incomplete strategy 13.46/3.12 % (2871386)Time elapsed: 0.002 s 13.46/3.12 % (2871386)Peak memory usage: 87 MB 13.46/3.12 % (2871390)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2071350010:cts=off:i=113:fsr=off:ss=included:sgt=4_1790 on theBenchmark for (1790ds/113Mi) 13.46/3.12 % (2871382)Instruction limit reached! 13.46/3.12 % (2871382)------------------------------ 13.46/3.12 % (2871382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871382)CaDiCaL version: 2.1.3 13.46/3.12 % (2871382)Termination reason: Instruction limit 13.46/3.12 % (2871382)Termination phase: Saturation 13.46/3.12 % (2871382)Time elapsed: 0.298 s 13.46/3.12 % (2871382)Peak memory usage: 90 MB 13.46/3.12 % (2871382)Instructions burned: 325 (million) 13.46/3.12 % (2871390)Instruction limit reached! 13.46/3.12 % (2871390)------------------------------ 13.46/3.12 % (2871390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871390)CaDiCaL version: 2.1.3 13.46/3.12 % (2871390)Termination reason: Instruction limit 13.46/3.12 % (2871390)Termination phase: Saturation 13.46/3.12 % (2871390)Time elapsed: 0.054 s 13.46/3.12 % (2871390)Peak memory usage: 88 MB 13.46/3.12 % (2871390)Instructions burned: 117 (million) 13.46/3.12 % (2871389)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2213037277:i=2350_1790 on theBenchmark for (1790ds/2350Mi) 13.46/3.12 % (2871367)First to succeed. 13.46/3.12 % (2871367)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2871361" 13.46/3.12 % (2871395)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3830612336:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_1787 on theBenchmark for (1787ds/114Mi) 13.46/3.12 % (2871386)------------------------------ 13.46/3.12 % (2871386)------------------------------ 13.46/3.12 % (2871395)Instruction limit reached! 13.46/3.12 % (2871395)------------------------------ 13.46/3.12 % (2871395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871395)CaDiCaL version: 2.1.3 13.46/3.12 % (2871395)Termination reason: Instruction limit 13.46/3.12 % (2871395)Termination phase: Saturation 13.46/3.12 % (2871395)Time elapsed: 0.055 s 13.46/3.12 % (2871395)Peak memory usage: 88 MB 13.46/3.12 % (2871395)Instructions burned: 115 (million) 13.46/3.12 % (2871393)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=111266677:i=127:av=off:fsr=off:sup=off_1787 on theBenchmark for (1787ds/127Mi) 13.46/3.12 % (2871393)Instruction limit reached! 13.46/3.12 % (2871393)------------------------------ 13.46/3.12 % (2871393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871393)CaDiCaL version: 2.1.3 13.46/3.12 % (2871393)Termination reason: Instruction limit 13.46/3.12 % (2871393)Termination phase: Saturation 13.46/3.12 % (2871393)Time elapsed: 0.106 s 13.46/3.12 % (2871393)Peak memory usage: 87 MB 13.46/3.12 % (2871393)Instructions burned: 127 (million) 13.46/3.12 % (2871398)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2575852865:i=437:sd=1:aac=none:ss=included_1784 on theBenchmark for (1784ds/437Mi) 13.46/3.12 % (2871398)Refutation not found, incomplete strategy 13.46/3.12 % (2871398)------------------------------ 13.46/3.12 % (2871398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 13.46/3.12 % (2871398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.46/3.12 % (2871398)CaDiCaL version: 2.1.3 13.46/3.12 % (2871398)Termination reason: Refutation not found, incomplete strategy 13.46/3.12 % (2871398)Time elapsed: 0.001 s 13.46/3.12 % (2871398)Peak memory usage: 88 MB 13.46/3.12 % (2871397)lrs+10_1_sil=8000:sp=occurrence:random_seed=2345012703:st=1.2:i=907:sd=14:ss=axioms:sgt=12_1784 on theBenchmark for (1784ds/907Mi) 13.46/3.12 % (2871367)Refutation found. Thanks to Tanya! 13.46/3.12 % SZS status Theorem for theBenchmark 13.46/3.12 % SZS output start Proof for theBenchmark 13.46/3.12 fof(f1,axiom,( 13.46/3.12 ! [X0,X1] : ((is_a_theorem(implies(X0,X1)) & is_a_theorem(X0)) => is_a_theorem(X1))), 13.46/3.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment)). 13.46/3.12 fof(f2,conjecture,( 13.46/3.12 is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z)))), 13.46/3.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3)). 13.46/3.12 fof(f3,negated_conjecture,( 13.46/3.12 ~is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z)))), 13.46/3.12 inference(negated_conjecture,[status(cth)],[f2])). 13.46/3.12 fof(f4,axiom,( 13.46/3.12 ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14] : is_a_theorem(implies(implies(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5),implies(implies(implies(implies(implies(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))),implies(implies(implies(n(X9),X9),X9),X10)),X10),implies(implies(X11,implies(n(X11),X12)),X13)),X13),X14)),X14))), 13.46/3.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f2)). 13.46/3.12 fof(f5,plain,( 13.46/3.12 ~is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z)))), 13.46/3.12 inference(flattening,[],[f3])). 13.46/3.12 fof(f6,plain,( 13.46/3.12 ! [X0,X1] : (is_a_theorem(X1) | (~is_a_theorem(implies(X0,X1)) | ~is_a_theorem(X0)))), 13.46/3.12 inference(ennf_transformation,[],[f1])). 13.46/3.12 fof(f7,plain,( 13.46/3.12 ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(implies(X0,X1)) | ~is_a_theorem(X0))), 13.46/3.12 inference(flattening,[],[f6])). 13.46/3.12 fof(f8,plain,( 13.46/3.12 ( ! [X0,X1] : (~is_a_theorem(implies(X0,X1)) | is_a_theorem(X1) | ~is_a_theorem(X0)) )), 13.46/3.12 inference(cnf_transformation,[],[f7])). 13.46/3.12 fof(f9,plain,( 13.46/3.12 ~is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z)))), 13.46/3.12 inference(cnf_transformation,[],[f5])). 13.46/3.12 fof(f10,plain,( 13.46/3.12 ( ! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] : (is_a_theorem(implies(implies(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5),implies(implies(implies(implies(implies(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))),implies(implies(implies(n(X9),X9),X9),X10)),X10),implies(implies(X11,implies(n(X11),X12)),X13)),X13),X14)),X14))) )), 13.46/3.12 inference(cnf_transformation,[],[f4])). 13.46/3.12 fof(f11,plain,( 13.46/3.12 ( ! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] : (~is_a_theorem(implies(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6),implies(implies(implies(implies(implies(implies(implies(X7,X8),implies(implies(X8,X9),implies(X7,X9))),implies(implies(implies(n(X10),X10),X10),X11)),X11),implies(implies(X12,implies(n(X12),X13)),X14)),X14),X0))) | is_a_theorem(X0)) )), 13.46/3.12 inference(resolution,[],[f10,f8])). 13.46/3.12 fof(f12,plain,( 13.46/3.12 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(X1,X0)))) )), 13.46/3.12 inference(resolution,[],[f11,f10])). 13.46/3.12 fof(f13,plain,( 13.46/3.12 ( ! [X2,X3,X0,X1,X4,X5] : (is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5))) )), 13.46/3.12 inference(resolution,[],[f12,f11])). 13.46/3.12 fof(f15,plain,( 13.46/3.12 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(X1,implies(X2,X1))))) )), 13.46/3.12 inference(resolution,[],[f13,f11])). 13.46/3.12 fof(f16,plain,( 13.46/3.12 ( ! [X2,X3,X0,X1,X4,X5] : (~is_a_theorem(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X0))) | is_a_theorem(X0)) )), 13.46/3.12 inference(resolution,[],[f13,f8])). 13.46/3.12 fof(f17,plain,( 13.46/3.12 ( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : (is_a_theorem(implies(X0,implies(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X8)),X8)))) )), 13.46/3.12 inference(resolution,[],[f15,f11])). 13.46/3.12 fof(f19,plain,( 13.46/3.12 ( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : (is_a_theorem(implies(implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4),implies(implies(X5,implies(n(X5),X6)),X7)),X7)) | ~is_a_theorem(X8)) )), 13.46/3.12 inference(resolution,[],[f17,f8])). 13.46/3.12 fof(f21,definition,( 13.46/3.12 spl0_1 <=> ! [X8] : ~is_a_theorem(X8)), 13.46/3.12 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])). 13.46/3.12 fof(f22,plain,( 13.46/3.12 ( ! [X8] : (~is_a_theorem(X8)) ) | ~spl0_1), 13.46/3.12 inference(avatar_component_clause,[],[f21])). 13.46/3.12 fof(f24,definition,( 13.46/3.12 spl0_2 <=> ! [X5,X4,X2,X7,X0,X6,X3,X1] : is_a_theorem(implies(implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4),implies(implies(X5,implies(n(X5),X6)),X7)),X7))), 13.46/3.12 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])). 13.46/3.12 fof(f25,plain,( 13.46/3.12 ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : (is_a_theorem(implies(implies(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4),implies(implies(X5,implies(n(X5),X6)),X7)),X7))) ) | ~spl0_2), 13.46/3.12 inference(avatar_component_clause,[],[f24])). 13.46/3.12 fof(f26,plain,( 13.46/3.12 spl0_1 | spl0_2), 13.46/3.12 inference(avatar_split_clause,[],[f19,f24,f21])). 13.46/3.12 fof(f28,plain,( 13.46/3.12 ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : (~is_a_theorem(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X0))) | is_a_theorem(X0)) ) | ~spl0_2), 13.46/3.12 inference(resolution,[],[f25,f8])). 13.46/3.12 fof(f31,plain,( 13.46/3.12 ( ! [X2,X3,X0,X1,X4] : (is_a_theorem(implies(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),implies(implies(implies(n(X3),X3),X3),X4)),X4))) ) | ~spl0_2), 13.46/3.12 inference(resolution,[],[f28,f12])). 13.46/3.12 fof(f35,plain,( 13.46/3.12 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),implies(X3,X2)))) ) | ~spl0_2), 13.46/3.12 inference(resolution,[],[f16,f31])). 13.46/3.12 fof(f39,plain,( 13.46/3.12 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(X1,implies(n(X1),X2))))) )), 13.46/3.12 inference(resolution,[],[f16,f17])). 13.46/3.12 fof(f43,plain,( 13.46/3.12 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))) ) | ~spl0_2), 13.46/3.12 inference(resolution,[],[f35,f28])). 13.46/3.12 fof(f49,plain,( 13.46/3.12 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) | ~is_a_theorem(implies(X2,X0))) ) | ~spl0_2), 13.46/3.12 inference(resolution,[],[f43,f8])). 13.46/3.12 fof(f50,plain,( 13.46/3.12 ~is_a_theorem(implies(implies(implies(y,u),x),implies(implies(x,y),y))) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f49,f9])). 14.04/3.49 fof(f54,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X1,X2)) | is_a_theorem(implies(X0,X2)) | ~is_a_theorem(implies(X0,X1))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f49,f8])). 14.04/3.49 fof(f60,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X3,X2)))) | ~is_a_theorem(implies(X0,implies(X3,X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f54,f43])). 14.04/3.49 fof(f62,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(X1,X2))) | ~is_a_theorem(implies(X0,X2))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f54,f12])). 14.04/3.49 fof(f73,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) | is_a_theorem(X2)) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f62,f16])). 14.04/3.49 fof(f81,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f73,f43])). 14.04/3.49 fof(f87,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1,X4] : (~is_a_theorem(implies(implies(X3,implies(X4,X3)),implies(X2,X0))) | is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f73,f60])). 14.04/3.49 fof(f92,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(X0,implies(implies(X3,X1),X2))) | is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f81,f54])). 14.04/3.49 fof(f93,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(implies(X2,X0),X1)) | is_a_theorem(implies(X0,X1))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f81,f8])). 14.04/3.49 fof(f107,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f87,f31])). 14.04/3.49 fof(f127,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(implies(implies(X1,X3),implies(X0,X3)),X2)) | is_a_theorem(implies(implies(X0,X1),X2))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f107,f8])). 14.04/3.49 fof(f136,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,X3)))) | ~is_a_theorem(implies(X2,implies(X1,X3)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f127,f49])). 14.04/3.49 fof(f147,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1,X4] : (is_a_theorem(implies(implies(X1,X4),implies(X0,implies(implies(X4,X2),X3)))) | ~is_a_theorem(implies(X0,implies(implies(X1,X2),X3)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f136,f127])). 14.04/3.49 fof(f186,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(implies(implies(n(X0),X0),X0),X1),X1))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f93,f31])). 14.04/3.49 fof(f219,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X0,X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f186,f127])). 14.04/3.49 fof(f239,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(n(X0),X1),implies(implies(X1,X0),X0)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f219,f127])). 14.04/3.49 fof(f241,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X0,implies(X1,implies(n(X2),X2)))) | is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f219,f54])). 14.04/3.49 fof(f246,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(implies(X0,X1),X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f239,f93])). 14.04/3.49 fof(f248,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(implies(X1,X2),X2))) | ~is_a_theorem(implies(X0,implies(n(X2),X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f239,f54])). 14.04/3.49 fof(f249,plain,( 14.04/3.49 ( ! [X0,X1] : (~is_a_theorem(implies(n(X1),X0)) | is_a_theorem(implies(implies(X0,X1),X1))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f239,f8])). 14.04/3.49 fof(f258,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(X1,X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f246,f92])). 14.04/3.49 fof(f260,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,X1),X1)) | ~is_a_theorem(X0)) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f246,f8])). 14.04/3.49 fof(f262,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(n(X0),X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f258,f28])). 14.04/3.49 fof(f273,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(implies(X0,X0),X1),X1))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f249,f258])). 14.04/3.49 fof(f285,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f273,f87])). 14.04/3.49 fof(f290,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X0,implies(implies(X2,X2),X1))) | is_a_theorem(implies(X0,X1))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f273,f54])). 14.04/3.49 fof(f305,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1,X4] : (~is_a_theorem(implies(implies(X4,X4),implies(implies(X0,X2),X3))) | is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),X3)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f290,f147])). 14.04/3.49 fof(f543,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),X3))) | ~is_a_theorem(implies(implies(X0,X2),X3))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f305,f49])). 14.04/3.49 fof(f550,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(X0,X0),X1),implies(implies(X1,X2),X2)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f305,f246])). 14.04/3.49 fof(f671,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1,X4] : (is_a_theorem(implies(implies(X4,X0),implies(implies(implies(X4,X1),X2),X3))) | ~is_a_theorem(implies(implies(implies(X0,X1),X2),X3))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f543,f127])). 14.04/3.49 fof(f689,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1,X4] : (~is_a_theorem(implies(implies(implies(X0,X1),X2),X3)) | is_a_theorem(implies(implies(X4,X0),implies(X2,X3)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f671,f92])). 14.04/3.49 fof(f807,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X2,X0),implies(X2,X1))) | ~is_a_theorem(implies(X0,X1))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f260,f127])). 14.04/3.49 fof(f837,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X0,implies(n(X1),X1))) | is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f807,f241])). 14.04/3.49 fof(f843,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,implies(implies(X1,X1),X2)),implies(X0,X2)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f837,f285])). 14.04/3.49 fof(f887,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(X0,implies(X1,implies(implies(X3,X3),X2)))) | is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f843,f54])). 14.04/3.49 fof(f904,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(X2,implies(implies(X0,X1),X3))) | is_a_theorem(implies(implies(X0,X1),implies(X2,X3)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f887,f147])). 14.04/3.49 fof(f1003,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X3,X1)))) | ~is_a_theorem(implies(X2,implies(X3,X0)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f904,f60])). 14.04/3.49 fof(f1094,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(X0,implies(implies(X1,X1),X2))) | is_a_theorem(implies(implies(X2,X3),implies(X0,X3)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f1003,f887])). 14.04/3.49 fof(f1152,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X2,implies(n(X0),X0))) | is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f1094,f248])). 14.04/3.49 fof(f1219,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(n(X0),X2)) | is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f1152,f49])). 14.04/3.49 fof(f1542,plain,( 14.04/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(X2,implies(implies(X2,X3),X3))))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f689,f550])). 14.04/3.49 fof(f1593,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f1542,f87])). 14.04/3.49 fof(f1635,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f1593,f127])). 14.04/3.49 fof(f1689,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X1,implies(X0,X2))) | is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f1635,f8])). 14.04/3.49 fof(f1742,plain,( 14.04/3.49 ( ! [X0,X1] : (is_a_theorem(implies(n(X0),implies(X0,X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f1689,f262])). 14.04/3.49 fof(f1745,plain,( 14.04/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X0),X1)))) ) | ~spl0_2), 14.04/3.49 inference(resolution,[],[f1742,f1219])). 14.04/3.49 fof(f1768,plain,( 14.04/3.49 $false | ~spl0_2), 14.04/3.49 inference(unit_resulting_resolution,[],[f305,f50,f1745])). 14.04/3.49 fof(f1790,plain,( 14.04/3.49 ~spl0_2), 14.04/3.49 inference(avatar_contradiction_clause,[],[f1768])). 14.04/3.49 fof(f1791,plain,( 14.04/3.49 $false | ~spl0_1), 14.04/3.49 inference(forward_subsumption_resolution,[],[f39,f22])). 14.04/3.49 fof(f1792,plain,( 14.04/3.49 ~spl0_1), 14.04/3.49 inference(avatar_contradiction_clause,[],[f1791])). 14.04/3.49 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f26])). 14.04/3.49 cnf(s4, plain, ~spl0_2, inference(sat_conversion,[],[f1790])). 14.04/3.49 cnf(s5, plain, ~spl0_1, inference(sat_conversion,[],[f1792])). 14.04/3.49 cnf(s6, plain, $false, inference(rat,[],[s1,s4,s5])). 14.04/3.49 fof(f1793,plain,( 14.04/3.49 $false), 14.04/3.49 inference(avatar_sat_refutation,[],[s6])). 14.04/3.49 % SZS output end Proof for theBenchmark 14.04/3.49 % (2871367)------------------------------ 14.04/3.49 % (2871367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 14.04/3.49 % (2871367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.04/3.49 % (2871367)CaDiCaL version: 2.1.3 14.04/3.49 % (2871367)Termination reason: Refutation 14.04/3.49 % (2871367)Time elapsed: 1.220 s 14.04/3.49 % (2871367)Peak memory usage: 133 MB 14.04/3.49 % (2871367)Instructions burned: 1524 (million) 14.04/3.49 % (2871367)------------------------------ 14.04/3.49 % (2871367)------------------------------ 14.04/3.49 % (2871361)Success in time 1.844 s 14.04/3.49 % Vampire exiting 14.04/3.50 EOF