0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.15/0.48 % Computer : n009.cluster.edu 0.15/0.48 % Model : x86_64 x86_64 0.15/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.48 % Memory : 8046.5625MB 0.15/0.48 % OS : Linux 6.8.0-71-generic 0.15/0.48 % CPULimit : 1440 0.15/0.48 % WCLimit : 180 0.15/0.48 % DateTime : Mon Jul 27 10:00:58 UTC 2026 0.15/0.48 % CPUTime : 0.15/0.49 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.20/0.54 Running first-order theorem proving 0.20/0.54 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p 8.60/3.18 % (963603)Detected formulas, will run a generic FOF schedule. 8.60/3.18 % (963612)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=82331055:i=119:av=off:ss=axioms_1799 on theBenchmark for (1799ds/119Mi) 8.60/3.18 % (963612)Refutation not found, incomplete strategy 8.60/3.18 % (963612)------------------------------ 8.60/3.18 % (963612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963612)CaDiCaL version: 2.1.3 8.60/3.18 % (963612)Termination reason: Refutation not found, incomplete strategy 8.60/3.18 % (963612)Time elapsed: 0.001 s 8.60/3.18 % (963612)Peak memory usage: 87 MB 8.60/3.18 % (963610)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=3082168508:i=141695:sd=1:nm=32:gsp=on:ss=included_1799 on theBenchmark for (1799ds/141695Mi) 8.60/3.18 % (963608)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=2663221592:i=141193_1799 on theBenchmark for (1799ds/141193Mi) 8.60/3.18 % (963609)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=1721487684:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_1799 on theBenchmark for (1799ds/134677Mi) 8.60/3.18 % (963611)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2586146730:i=109:sd=1:ins=1:gsp=on:ss=axioms_1799 on theBenchmark for (1799ds/109Mi) 8.60/3.18 % (963611)Refutation not found, incomplete strategy 8.60/3.18 % (963611)------------------------------ 8.60/3.18 % (963611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963611)CaDiCaL version: 2.1.3 8.60/3.18 % (963611)Termination reason: Refutation not found, incomplete strategy 8.60/3.18 % (963611)Time elapsed: 0.001 s 8.60/3.18 % (963611)Peak memory usage: 87 MB 8.60/3.18 % (963613)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=782834121:s2a=on:i=139:gtg=position_1799 on theBenchmark for (1799ds/139Mi) 8.60/3.18 % (963614)dis-21_1_sil=8000:lcm=predicate:random_seed=1889634104: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) 8.60/3.18 % (963614)Instruction limit reached! 8.60/3.18 % (963614)------------------------------ 8.60/3.18 % (963614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963614)CaDiCaL version: 2.1.3 8.60/3.18 % (963614)Termination reason: Instruction limit 8.60/3.18 % (963614)Termination phase: Saturation 8.60/3.18 % (963614)Time elapsed: 0.124 s 8.60/3.18 % (963614)Peak memory usage: 89 MB 8.60/3.18 % (963614)Instructions burned: 129 (million) 8.60/3.18 % (963613)Instruction limit reached! 8.60/3.18 % (963613)------------------------------ 8.60/3.18 % (963613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963613)CaDiCaL version: 2.1.3 8.60/3.18 % (963613)Termination reason: Instruction limit 8.60/3.18 % (963613)Termination phase: Saturation 8.60/3.18 % (963613)Time elapsed: 0.125 s 8.60/3.18 % (963613)Peak memory usage: 88 MB 8.60/3.18 % (963613)Instructions burned: 140 (million) 8.60/3.18 % (963612)------------------------------ 8.60/3.18 % (963612)------------------------------ 8.60/3.18 % (963611)------------------------------ 8.60/3.18 % (963611)------------------------------ 8.60/3.18 % (963624)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4140094695:i=325:sd=1:ss=axioms:sgt=32_1795 on theBenchmark for (1795ds/325Mi) 8.60/3.18 % (963623)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2934771889:i=157:sd=1:gtg=position:ss=axioms:sgt=8_1795 on theBenchmark for (1795ds/157Mi) 8.60/3.18 % (963622)lrs+10_1_sil=8000:sp=occurrence:random_seed=199054647:i=285:sd=3:ss=axioms:sgt=8_1795 on theBenchmark for (1795ds/285Mi) 8.60/3.18 % (963623)Instruction limit reached! 8.60/3.18 % (963623)------------------------------ 8.60/3.18 % (963623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963623)CaDiCaL version: 2.1.3 8.60/3.18 % (963623)Termination reason: Instruction limit 8.60/3.18 % (963623)Termination phase: Saturation 8.60/3.18 % (963623)Time elapsed: 0.139 s 8.60/3.18 % (963623)Peak memory usage: 88 MB 8.60/3.18 % (963623)Instructions burned: 157 (million) 8.60/3.18 % (963624)Instruction limit reached! 8.60/3.18 % (963624)------------------------------ 8.60/3.18 % (963624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963624)CaDiCaL version: 2.1.3 8.60/3.18 % (963624)Termination reason: Instruction limit 8.60/3.18 % (963624)Termination phase: Saturation 8.60/3.18 % (963624)Time elapsed: 0.156 s 8.60/3.18 % (963624)Peak memory usage: 90 MB 8.60/3.18 % (963624)Instructions burned: 326 (million) 8.60/3.18 % (963625)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=3430902673:s2a=on:i=248:s2at=1.23:gtg=position_1793 on theBenchmark for (1793ds/248Mi) 8.60/3.18 % (963622)Instruction limit reached! 8.60/3.18 % (963622)------------------------------ 8.60/3.18 % (963622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963622)CaDiCaL version: 2.1.3 8.60/3.18 % (963622)Termination reason: Instruction limit 8.60/3.18 % (963622)Termination phase: Saturation 8.60/3.18 % (963622)Time elapsed: 0.292 s 8.60/3.18 % (963622)Peak memory usage: 91 MB 8.60/3.18 % (963622)Instructions burned: 285 (million) 8.60/3.18 % (963630)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1896654863:i=2350_1791 on theBenchmark for (1791ds/2350Mi) 8.60/3.18 % (963625)Instruction limit reached! 8.60/3.18 % (963625)------------------------------ 8.60/3.18 % (963625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963625)CaDiCaL version: 2.1.3 8.60/3.18 % (963625)Termination reason: Instruction limit 8.60/3.18 % (963625)Termination phase: Saturation 8.60/3.18 % (963625)Time elapsed: 0.207 s 8.60/3.18 % (963625)Peak memory usage: 88 MB 8.60/3.18 % (963625)Instructions burned: 249 (million) 8.60/3.18 % (963629)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3883977812:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_1792 on theBenchmark for (1792ds/294Mi) 8.60/3.18 % (963629)Refutation not found, incomplete strategy 8.60/3.18 % (963629)------------------------------ 8.60/3.18 % (963629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963629)CaDiCaL version: 2.1.3 8.60/3.18 % (963629)Termination reason: Refutation not found, incomplete strategy 8.60/3.18 % (963629)Time elapsed: 0.001 s 8.60/3.18 % (963629)Peak memory usage: 87 MB 8.60/3.18 % (963632)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=437120668:cts=off:i=113:fsr=off:ss=included:sgt=4_1790 on theBenchmark for (1790ds/113Mi) 8.60/3.18 % (963632)Instruction limit reached! 8.60/3.18 % (963632)------------------------------ 8.60/3.18 % (963632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963632)CaDiCaL version: 2.1.3 8.60/3.18 % (963632)Termination reason: Instruction limit 8.60/3.18 % (963632)Termination phase: Saturation 8.60/3.18 % (963632)Time elapsed: 0.096 s 8.60/3.18 % (963632)Peak memory usage: 88 MB 8.60/3.18 % (963632)Instructions burned: 113 (million) 8.60/3.18 % (963635)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=926637292:i=127:av=off:fsr=off:sup=off_1789 on theBenchmark for (1789ds/127Mi) 8.60/3.18 % (963629)------------------------------ 8.60/3.18 % (963629)------------------------------ 8.60/3.18 % (963635)Instruction limit reached! 8.60/3.18 % (963635)------------------------------ 8.60/3.18 % (963635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963635)CaDiCaL version: 2.1.3 8.60/3.18 % (963635)Termination reason: Instruction limit 8.60/3.18 % (963635)Termination phase: Saturation 8.60/3.18 % (963635)Time elapsed: 0.104 s 8.60/3.18 % (963635)Peak memory usage: 87 MB 8.60/3.18 % (963635)Instructions burned: 128 (million) 8.60/3.18 % (963609)First to succeed. 8.60/3.18 % (963609)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-963603" 8.60/3.18 % (963637)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3453083800:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_1786 on theBenchmark for (1786ds/114Mi) 8.60/3.18 % (963639)lrs+10_1_sil=8000:sp=occurrence:random_seed=1439192905:st=1.2:i=907:sd=14:ss=axioms:sgt=12_1785 on theBenchmark for (1785ds/907Mi) 8.60/3.18 % (963637)Instruction limit reached! 8.60/3.18 % (963637)------------------------------ 8.60/3.18 % (963637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963637)CaDiCaL version: 2.1.3 8.60/3.18 % (963637)Termination reason: Instruction limit 8.60/3.18 % (963637)Termination phase: Saturation 8.60/3.18 % (963637)Time elapsed: 0.102 s 8.60/3.18 % (963637)Peak memory usage: 88 MB 8.60/3.18 % (963637)Instructions burned: 114 (million) 8.60/3.18 % (963640)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3523473440:i=437:sd=1:aac=none:ss=included_1785 on theBenchmark for (1785ds/437Mi) 8.60/3.18 % (963640)Refutation not found, incomplete strategy 8.60/3.18 % (963640)------------------------------ 8.60/3.18 % (963640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 8.60/3.18 % (963640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.60/3.18 % (963640)CaDiCaL version: 2.1.3 8.60/3.18 % (963640)Termination reason: Refutation not found, incomplete strategy 8.60/3.18 % (963640)Time elapsed: 0.001 s 8.60/3.18 % (963640)Peak memory usage: 88 MB 8.60/3.18 % (963609)Refutation found. Thanks to Tanya! 8.60/3.18 % SZS status Theorem for theBenchmark 8.60/3.18 % SZS output start Proof for theBenchmark 8.60/3.18 fof(f1,axiom,( 8.60/3.18 ! [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))), 8.60/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p',f2)). 8.60/3.18 fof(f2,axiom,( 8.60/3.18 ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(implies(X0,X1))) => is_a_theorem(X1))), 8.60/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment)). 8.60/3.18 fof(f3,conjecture,( 8.60/3.18 is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z))))), 8.60/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p',f3)). 8.60/3.18 fof(f4,negated_conjecture,( 8.60/3.18 ~is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z))))), 8.60/3.18 inference(negated_conjecture,[status(cth)],[f3])). 8.60/3.18 fof(f5,plain,( 8.60/3.18 ~is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z))))), 8.60/3.18 inference(flattening,[],[f4])). 8.60/3.18 fof(f6,plain,( 8.60/3.18 ! [X0,X1] : (is_a_theorem(X1) | (~is_a_theorem(X0) | ~is_a_theorem(implies(X0,X1))))), 8.60/3.18 inference(ennf_transformation,[],[f2])). 8.60/3.18 fof(f7,plain,( 8.60/3.18 ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(X0) | ~is_a_theorem(implies(X0,X1)))), 8.60/3.18 inference(flattening,[],[f6])). 8.60/3.18 fof(f8,plain,( 8.60/3.18 ( ! [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))) )), 8.60/3.18 inference(cnf_transformation,[],[f1])). 8.60/3.18 fof(f9,plain,( 8.60/3.18 ( ! [X0,X1] : (~is_a_theorem(implies(X0,X1)) | ~is_a_theorem(X0) | is_a_theorem(X1)) )), 8.60/3.18 inference(cnf_transformation,[],[f7])). 8.60/3.18 fof(f10,plain,( 8.60/3.18 ~is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z))))), 8.60/3.18 inference(cnf_transformation,[],[f5])). 8.60/3.18 fof(f11,plain,( 8.60/3.18 ( ! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] : (~is_a_theorem(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))) | is_a_theorem(X14)) )), 14.48/3.49 inference(resolution,[],[f8,f9])). 14.48/3.49 fof(f12,plain,( 14.48/3.49 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(X1,X0)))) )), 14.48/3.49 inference(resolution,[],[f11,f8])). 14.48/3.49 fof(f13,plain,( 14.48/3.49 ( ! [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))) )), 14.48/3.49 inference(resolution,[],[f12,f11])). 14.48/3.49 fof(f15,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(X1,implies(X2,X1))))) )), 14.48/3.49 inference(resolution,[],[f13,f11])). 14.48/3.49 fof(f16,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1,X4,X5] : (~is_a_theorem(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5))) | is_a_theorem(X5)) )), 14.48/3.49 inference(resolution,[],[f13,f9])). 14.48/3.49 fof(f17,plain,( 14.48/3.49 ( ! [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)))) )), 14.48/3.49 inference(resolution,[],[f15,f11])). 14.48/3.49 fof(f19,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : (~is_a_theorem(X0) | is_a_theorem(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))) )), 14.48/3.49 inference(resolution,[],[f17,f9])). 14.48/3.49 fof(f21,definition,( 14.48/3.49 spl0_1 <=> ! [X5,X3,X4,X2,X7,X6,X8,X1] : is_a_theorem(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))), 14.48/3.49 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])). 14.48/3.49 fof(f22,plain,( 14.48/3.49 ( ! [X2,X3,X1,X8,X6,X7,X4,X5] : (is_a_theorem(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))) ) | ~spl0_1), 14.48/3.49 inference(avatar_component_clause,[],[f21])). 14.48/3.49 fof(f24,definition,( 14.48/3.49 spl0_2 <=> ! [X0] : ~is_a_theorem(X0)), 14.48/3.49 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])). 14.48/3.49 fof(f25,plain,( 14.48/3.49 ( ! [X0] : (~is_a_theorem(X0)) ) | ~spl0_2), 14.48/3.49 inference(avatar_component_clause,[],[f24])). 14.48/3.49 fof(f26,plain,( 14.48/3.49 spl0_1 | spl0_2), 14.48/3.49 inference(avatar_split_clause,[],[f19,f24,f21])). 14.48/3.49 fof(f33,plain,( 14.48/3.49 $false | ~spl0_2), 14.48/3.49 inference(unit_resulting_resolution,[],[f9,f8,f17,f25])). 14.48/3.49 fof(f50,plain,( 14.48/3.49 ~spl0_2), 14.48/3.49 inference(avatar_contradiction_clause,[],[f33])). 14.48/3.49 fof(f52,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : (~is_a_theorem(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))) | is_a_theorem(X7)) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f22,f9])). 14.48/3.49 fof(f55,plain,( 14.48/3.49 ( ! [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_1), 14.48/3.49 inference(resolution,[],[f52,f12])). 14.48/3.49 fof(f59,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),implies(X3,X2)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f16,f55])). 14.48/3.49 fof(f67,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f59,f52])). 14.48/3.49 fof(f73,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X1,X2),implies(X0,X2))) | ~is_a_theorem(implies(X0,X1))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f67,f9])). 14.48/3.49 fof(f77,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X1,X2)) | ~is_a_theorem(implies(X0,X1)) | is_a_theorem(implies(X0,X2))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f73,f9])). 14.48/3.49 fof(f83,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(X0,implies(implies(X2,X3),implies(X1,X3)))) | ~is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f77,f67])). 14.48/3.49 fof(f85,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(X2,X1))) | ~is_a_theorem(implies(X0,X1))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f77,f12])). 14.48/3.49 fof(f96,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) | is_a_theorem(X2)) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f85,f16])). 14.48/3.49 fof(f104,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f96,f67])). 14.48/3.49 fof(f110,plain,( 14.48/3.49 ( ! [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_1), 14.48/3.49 inference(resolution,[],[f96,f83])). 14.48/3.49 fof(f115,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(X0,implies(implies(X1,X2),X3))) | is_a_theorem(implies(X0,implies(X2,X3)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f104,f77])). 14.48/3.49 fof(f116,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(implies(X0,X1),X2)) | is_a_theorem(implies(X1,X2))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f104,f9])). 14.48/3.49 fof(f130,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f110,f55])). 14.48/3.49 fof(f150,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)) | is_a_theorem(implies(implies(X2,X0),X3))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f130,f9])). 14.48/3.49 fof(f159,plain,( 14.48/3.49 ( ! [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_1), 14.48/3.49 inference(resolution,[],[f150,f73])). 14.48/3.49 fof(f170,plain,( 14.48/3.49 ( ! [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_1), 14.48/3.49 inference(resolution,[],[f159,f150])). 14.48/3.49 fof(f209,plain,( 14.48/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(implies(implies(n(X0),X0),X0),X1),X1))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f116,f55])). 14.48/3.49 fof(f242,plain,( 14.48/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X0,X1)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f209,f150])). 14.48/3.49 fof(f262,plain,( 14.48/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(n(X0),X1),implies(implies(X1,X0),X0)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f242,f150])). 14.48/3.49 fof(f264,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X0,implies(X1,implies(n(X2),X2)))) | is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f242,f77])). 14.48/3.49 fof(f269,plain,( 14.48/3.49 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(implies(X0,X1),X1)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f262,f116])). 14.48/3.49 fof(f272,plain,( 14.48/3.49 ( ! [X0,X1] : (~is_a_theorem(implies(n(X0),X1)) | is_a_theorem(implies(implies(X1,X0),X0))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f262,f9])). 14.48/3.49 fof(f281,plain,( 14.48/3.49 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(X1,X1)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f269,f115])). 14.48/3.49 fof(f283,plain,( 14.48/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,X1),X1)) | ~is_a_theorem(X0)) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f269,f9])). 14.48/3.49 fof(f296,plain,( 14.48/3.49 ( ! [X0,X1] : (is_a_theorem(implies(implies(implies(X0,X0),X1),X1))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f272,f281])). 14.48/3.49 fof(f331,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f296,f110])). 14.48/3.49 fof(f845,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X2,X0),implies(X2,X1))) | ~is_a_theorem(implies(X0,X1))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f283,f150])). 14.48/3.49 fof(f875,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X0,implies(n(X1),X1))) | is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f845,f264])). 14.48/3.49 fof(f881,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,implies(implies(X1,X1),X2)),implies(X0,X2)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f875,f331])). 14.48/3.49 fof(f925,plain,( 14.48/3.49 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(X0,implies(X1,implies(implies(X2,X2),X3)))) | is_a_theorem(implies(X0,implies(X1,X3)))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f881,f77])). 14.48/3.49 fof(f942,plain,( 14.48/3.49 ( ! [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_1), 14.48/3.49 inference(resolution,[],[f925,f170])). 14.48/3.49 fof(f1025,plain,( 14.48/3.49 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))) ) | ~spl0_1), 14.48/3.49 inference(resolution,[],[f942,f67])). 14.48/3.49 fof(f1054,plain,( 14.48/3.49 $false | ~spl0_1), 14.48/3.49 inference(unit_resulting_resolution,[],[f77,f10,f130,f1025])). 14.48/3.49 fof(f1075,plain,( 14.48/3.49 ~spl0_1), 14.48/3.49 inference(avatar_contradiction_clause,[],[f1054])). 14.48/3.49 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f26])). 14.48/3.49 cnf(s13, plain, ~spl0_2, inference(sat_conversion,[],[f50])). 14.48/3.49 cnf(s14, plain, ~spl0_1, inference(sat_conversion,[],[f1075])). 14.48/3.49 cnf(s15, plain, $false, inference(rat,[],[s1,s13,s14])). 14.48/3.49 fof(f1076,plain,( 14.48/3.49 $false), 14.48/3.49 inference(avatar_sat_refutation,[],[s15])). 14.48/3.49 % SZS output end Proof for theBenchmark 14.48/3.49 % (963609)------------------------------ 14.48/3.49 % (963609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 14.48/3.49 % (963609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.48/3.49 % (963609)CaDiCaL version: 2.1.3 14.48/3.49 % (963609)Termination reason: Refutation 14.48/3.49 % (963609)Time elapsed: 1.294 s 14.48/3.49 % (963609)Peak memory usage: 131 MB 14.48/3.49 % (963609)Instructions burned: 1288 (million) 14.48/3.49 % (963609)------------------------------ 14.48/3.49 % (963609)------------------------------ 14.48/3.49 % (963603)Success in time 1.952 s 14.48/3.49 % Vampire exiting 14.65/3.50 EOF