0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.09/0.37 % Computer : n027.cluster.edu 0.09/0.37 % Model : x86_64 x86_64 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.37 % Memory : 8046.5625MB 0.09/0.37 % OS : Linux 6.8.0-71-generic 0.09/0.37 % CPULimit : 1440 0.09/0.37 % WCLimit : 180 0.09/0.37 % DateTime : Mon Jul 27 10:11:53 UTC 2026 0.09/0.38 % CPUTime : 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.09/0.42 Running first-order theorem proving 0.09/0.42 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 6.66/1.87 % (2903568)Detected formulas, will run a generic FOF schedule. 6.66/1.87 % (2903578)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1489247630:s2a=on:i=139:gtg=position_1799 on theBenchmark for (1799ds/139Mi) 6.66/1.87 % (2903575)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=2926503405:i=141695:sd=1:nm=32:gsp=on:ss=included_1799 on theBenchmark for (1799ds/141695Mi) 6.66/1.87 % (2903577)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1974263760:i=119:av=off:ss=axioms_1799 on theBenchmark for (1799ds/119Mi) 6.66/1.87 % (2903576)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=79484975:i=109:sd=1:ins=1:gsp=on:ss=axioms_1799 on theBenchmark for (1799ds/109Mi) 6.66/1.87 % (2903573)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=2894215978:i=141193_1799 on theBenchmark for (1799ds/141193Mi) 6.66/1.87 % (2903579)dis-21_1_sil=8000:lcm=predicate:random_seed=3328216940: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) 6.66/1.87 % (2903574)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=1659823991:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_1799 on theBenchmark for (1799ds/134677Mi) 6.66/1.87 % (2903576)Refutation not found, incomplete strategy 6.66/1.87 % (2903576)------------------------------ 6.66/1.87 % (2903576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903576)CaDiCaL version: 2.1.3 6.66/1.87 % (2903576)Termination reason: Refutation not found, incomplete strategy 6.66/1.87 % (2903576)Time elapsed: 0.001 s 6.66/1.87 % (2903576)Peak memory usage: 87 MB 6.66/1.87 % (2903577)Instruction limit reached! 6.66/1.87 % (2903577)------------------------------ 6.66/1.87 % (2903577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903577)CaDiCaL version: 2.1.3 6.66/1.87 % (2903577)Termination reason: Instruction limit 6.66/1.87 % (2903577)Termination phase: Saturation 6.66/1.87 % (2903577)Time elapsed: 0.074 s 6.66/1.87 % (2903577)Peak memory usage: 88 MB 6.66/1.87 % (2903577)Instructions burned: 119 (million) 6.66/1.87 % (2903579)Instruction limit reached! 6.66/1.87 % (2903579)------------------------------ 6.66/1.87 % (2903579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903579)CaDiCaL version: 2.1.3 6.66/1.87 % (2903579)Termination reason: Instruction limit 6.66/1.87 % (2903579)Termination phase: Saturation 6.66/1.87 % (2903579)Time elapsed: 0.084 s 6.66/1.87 % (2903579)Peak memory usage: 89 MB 6.66/1.87 % (2903579)Instructions burned: 130 (million) 6.66/1.87 % (2903578)Instruction limit reached! 6.66/1.87 % (2903578)------------------------------ 6.66/1.87 % (2903578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903578)CaDiCaL version: 2.1.3 6.66/1.87 % (2903578)Termination reason: Instruction limit 6.66/1.87 % (2903578)Termination phase: Saturation 6.66/1.87 % (2903578)Time elapsed: 0.087 s 6.66/1.87 % (2903578)Peak memory usage: 89 MB 6.66/1.87 % (2903578)Instructions burned: 140 (million) 6.66/1.87 % (2903589)lrs+1011_1_sil=32000:sp=occurrence:random_seed=719905627:i=325:sd=1:ss=axioms:sgt=32_1797 on theBenchmark for (1797ds/325Mi) 6.66/1.87 % (2903587)lrs+10_1_sil=8000:sp=occurrence:random_seed=146818129:i=285:sd=3:ss=axioms:sgt=8_1797 on theBenchmark for (1797ds/285Mi) 6.66/1.87 % (2903588)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2765537629:i=157:sd=1:gtg=position:ss=axioms:sgt=8_1797 on theBenchmark for (1797ds/157Mi) 6.66/1.87 % (2903576)------------------------------ 6.66/1.87 % (2903576)------------------------------ 6.66/1.87 % (2903589)Instruction limit reached! 6.66/1.87 % (2903589)------------------------------ 6.66/1.87 % (2903589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903589)CaDiCaL version: 2.1.3 6.66/1.87 % (2903589)Termination reason: Instruction limit 6.66/1.87 % (2903589)Termination phase: Saturation 6.66/1.87 % (2903589)Time elapsed: 0.104 s 6.66/1.87 % (2903589)Peak memory usage: 90 MB 6.66/1.87 % (2903589)Instructions burned: 326 (million) 6.66/1.87 % (2903588)Instruction limit reached! 6.66/1.87 % (2903588)------------------------------ 6.66/1.87 % (2903588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903588)CaDiCaL version: 2.1.3 6.66/1.87 % (2903588)Termination reason: Instruction limit 6.66/1.87 % (2903588)Termination phase: Saturation 6.66/1.87 % (2903588)Time elapsed: 0.090 s 6.66/1.87 % (2903588)Peak memory usage: 88 MB 6.66/1.87 % (2903588)Instructions burned: 158 (million) 6.66/1.87 % (2903594)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2716626371:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_1795 on theBenchmark for (1795ds/294Mi) 6.66/1.87 % (2903594)Refutation not found, incomplete strategy 6.66/1.87 % (2903594)------------------------------ 6.66/1.87 % (2903594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903594)CaDiCaL version: 2.1.3 6.66/1.87 % (2903594)Termination reason: Refutation not found, incomplete strategy 6.66/1.87 % (2903594)Time elapsed: 0.0000 s 6.66/1.87 % (2903594)Peak memory usage: 87 MB 6.66/1.87 % (2903593)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=582554644:s2a=on:i=248:s2at=1.23:gtg=position_1796 on theBenchmark for (1796ds/248Mi) 6.66/1.87 % (2903587)Instruction limit reached! 6.66/1.87 % (2903587)------------------------------ 6.66/1.87 % (2903587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903587)CaDiCaL version: 2.1.3 6.66/1.87 % (2903587)Termination reason: Instruction limit 6.66/1.87 % (2903587)Termination phase: Saturation 6.66/1.87 % (2903587)Time elapsed: 0.184 s 6.66/1.87 % (2903587)Peak memory usage: 91 MB 6.66/1.87 % (2903587)Instructions burned: 286 (million) 6.66/1.87 % (2903595)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4258663414:i=2350_1795 on theBenchmark for (1795ds/2350Mi) 6.66/1.87 % (2903594)------------------------------ 6.66/1.87 % (2903594)------------------------------ 6.66/1.87 % (2903593)Instruction limit reached! 6.66/1.87 % (2903593)------------------------------ 6.66/1.87 % (2903593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903593)CaDiCaL version: 2.1.3 6.66/1.87 % (2903593)Termination reason: Instruction limit 6.66/1.87 % (2903593)Termination phase: Saturation 6.66/1.87 % (2903593)Time elapsed: 0.142 s 6.66/1.87 % (2903593)Peak memory usage: 88 MB 6.66/1.87 % (2903593)Instructions burned: 248 (million) 6.66/1.87 % (2903598)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=726661751:cts=off:i=113:fsr=off:ss=included:sgt=4_1794 on theBenchmark for (1794ds/113Mi) 6.66/1.87 % (2903598)Instruction limit reached! 6.66/1.87 % (2903598)------------------------------ 6.66/1.87 % (2903598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903598)CaDiCaL version: 2.1.3 6.66/1.87 % (2903598)Termination reason: Instruction limit 6.66/1.87 % (2903598)Termination phase: Saturation 6.66/1.87 % (2903598)Time elapsed: 0.063 s 6.66/1.87 % (2903598)Peak memory usage: 88 MB 6.66/1.87 % (2903598)Instructions burned: 113 (million) 6.66/1.87 % (2903600)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=946971350:i=127:av=off:fsr=off:sup=off_1793 on theBenchmark for (1793ds/127Mi) 6.66/1.87 % (2903602)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=241642354:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_1793 on theBenchmark for (1793ds/114Mi) 6.66/1.87 % (2903600)Instruction limit reached! 6.66/1.87 % (2903600)------------------------------ 6.66/1.87 % (2903600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903600)CaDiCaL version: 2.1.3 6.66/1.87 % (2903600)Termination reason: Instruction limit 6.66/1.87 % (2903600)Termination phase: Saturation 6.66/1.87 % (2903600)Time elapsed: 0.069 s 6.66/1.87 % (2903600)Peak memory usage: 87 MB 6.66/1.87 % (2903600)Instructions burned: 128 (million) 6.66/1.87 % (2903602)Instruction limit reached! 6.66/1.87 % (2903602)------------------------------ 6.66/1.87 % (2903602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903602)CaDiCaL version: 2.1.3 6.66/1.87 % (2903602)Termination reason: Instruction limit 6.66/1.87 % (2903602)Termination phase: Saturation 6.66/1.87 % (2903602)Time elapsed: 0.062 s 6.66/1.87 % (2903602)Peak memory usage: 88 MB 6.66/1.87 % (2903602)Instructions burned: 114 (million) 6.66/1.87 % (2903603)lrs+10_1_sil=8000:sp=occurrence:random_seed=1078996957:st=1.2:i=907:sd=14:ss=axioms:sgt=12_1792 on theBenchmark for (1792ds/907Mi) 6.66/1.87 % (2903606)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=354325821:i=437:sd=1:aac=none:ss=included_1791 on theBenchmark for (1791ds/437Mi) 6.66/1.87 % (2903606)Refutation not found, incomplete strategy 6.66/1.87 % (2903606)------------------------------ 6.66/1.87 % (2903606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 6.66/1.87 % (2903606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.66/1.87 % (2903606)CaDiCaL version: 2.1.3 6.66/1.87 % (2903606)Termination reason: Refutation not found, incomplete strategy 6.66/1.87 % (2903606)Time elapsed: 0.001 s 6.66/1.87 % (2903606)Peak memory usage: 88 MB 6.66/1.87 % (2903608)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1025577107:i=5202:ss=axioms:sgt=16_1791 on theBenchmark for (1791ds/5202Mi) 6.66/1.87 % (2903574)First to succeed. 6.66/1.87 % (2903574)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2903568" 6.66/1.87 % (2903606)------------------------------ 6.66/1.87 % (2903606)------------------------------ 6.66/1.87 % (2903574)Refutation found. Thanks to Tanya! 6.66/1.87 % SZS status Theorem for theBenchmark 6.66/1.87 % SZS output start Proof for theBenchmark 6.66/1.87 fof(f1,axiom,( 6.66/1.87 ! [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))), 6.66/1.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p',f2)). 6.66/1.87 fof(f2,axiom,( 6.66/1.87 ! [X0,X1] : ((is_a_theorem(implies(X0,X1)) & is_a_theorem(X0)) => is_a_theorem(X1))), 6.66/1.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment)). 6.66/1.87 fof(f3,conjecture,( 6.66/1.87 is_a_theorem(implies(implies(x,y),implies(implies(y,n(x)),n(x))))), 6.66/1.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p',f3)). 6.66/1.87 fof(f4,negated_conjecture,( 6.66/1.87 ~is_a_theorem(implies(implies(x,y),implies(implies(y,n(x)),n(x))))), 6.66/1.87 inference(negated_conjecture,[status(cth)],[f3])). 6.66/1.87 fof(f5,plain,( 6.66/1.87 ~is_a_theorem(implies(implies(x,y),implies(implies(y,n(x)),n(x))))), 6.66/1.87 inference(flattening,[],[f4])). 6.66/1.87 fof(f6,plain,( 6.66/1.87 ! [X0,X1] : (is_a_theorem(X1) | (~is_a_theorem(implies(X0,X1)) | ~is_a_theorem(X0)))), 6.66/1.87 inference(ennf_transformation,[],[f2])). 6.66/1.87 fof(f7,plain,( 6.66/1.87 ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(implies(X0,X1)) | ~is_a_theorem(X0))), 6.66/1.87 inference(flattening,[],[f6])). 6.66/1.87 fof(f8,plain,( 6.66/1.87 ( ! [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))) )), 6.66/1.87 inference(cnf_transformation,[],[f1])). 6.66/1.87 fof(f9,plain,( 6.66/1.87 ( ! [X0,X1] : (~is_a_theorem(implies(X0,X1)) | is_a_theorem(X1) | ~is_a_theorem(X0)) )), 9.25/2.06 inference(cnf_transformation,[],[f7])). 9.25/2.06 fof(f10,plain,( 9.25/2.06 ~is_a_theorem(implies(implies(x,y),implies(implies(y,n(x)),n(x))))), 9.25/2.06 inference(cnf_transformation,[],[f5])). 9.25/2.06 fof(f11,plain,( 9.25/2.06 ( ! [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)) )), 9.25/2.06 inference(resolution,[],[f8,f9])). 9.25/2.06 fof(f12,plain,( 9.25/2.06 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(X1,X0)))) )), 9.25/2.06 inference(resolution,[],[f11,f8])). 9.25/2.06 fof(f13,plain,( 9.25/2.06 ( ! [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))) )), 9.25/2.06 inference(resolution,[],[f12,f11])). 9.25/2.06 fof(f15,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(X1,implies(X2,X1))))) )), 9.25/2.06 inference(resolution,[],[f13,f11])). 9.25/2.06 fof(f16,plain,( 9.25/2.06 ( ! [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)) )), 9.25/2.06 inference(resolution,[],[f13,f9])). 9.25/2.06 fof(f17,plain,( 9.25/2.06 ( ! [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)))) )), 9.25/2.06 inference(resolution,[],[f15,f11])). 9.25/2.06 fof(f19,plain,( 9.25/2.06 ( ! [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)) )), 9.25/2.06 inference(resolution,[],[f17,f9])). 9.25/2.06 fof(f21,definition,( 9.25/2.06 spl0_1 <=> ! [X8] : ~is_a_theorem(X8)), 9.25/2.06 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])). 9.25/2.06 fof(f22,plain,( 9.25/2.06 ( ! [X8] : (~is_a_theorem(X8)) ) | ~spl0_1), 9.25/2.06 inference(avatar_component_clause,[],[f21])). 9.25/2.06 fof(f24,definition,( 9.25/2.06 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))), 9.25/2.06 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])). 9.25/2.06 fof(f25,plain,( 9.25/2.06 ( ! [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), 9.25/2.06 inference(avatar_component_clause,[],[f24])). 9.25/2.06 fof(f26,plain,( 9.25/2.06 spl0_1 | spl0_2), 9.25/2.06 inference(avatar_split_clause,[],[f19,f24,f21])). 9.25/2.06 fof(f28,plain,( 9.25/2.06 ( ! [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), 9.25/2.06 inference(resolution,[],[f25,f9])). 9.25/2.06 fof(f31,plain,( 9.25/2.06 ( ! [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), 9.25/2.06 inference(resolution,[],[f28,f12])). 9.25/2.06 fof(f32,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(X1,implies(n(X1),X2))))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f28,f15])). 9.25/2.06 fof(f54,plain,( 9.25/2.06 $false | ~spl0_1), 9.25/2.06 inference(resolution,[],[f22,f13])). 9.25/2.06 fof(f67,plain,( 9.25/2.06 ~spl0_1), 9.25/2.06 inference(avatar_contradiction_clause,[],[f54])). 9.25/2.06 fof(f81,plain,( 9.25/2.06 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),implies(X3,X2)))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f16,f31])). 9.25/2.06 fof(f83,plain,( 9.25/2.06 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(implies(n(X1),X1),X1)))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f16,f25])). 9.25/2.06 fof(f96,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f81,f28])). 9.25/2.06 fof(f102,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) | ~is_a_theorem(implies(X2,X0))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f96,f9])). 9.25/2.06 fof(f106,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X1,X2)) | is_a_theorem(implies(X0,X2)) | ~is_a_theorem(implies(X0,X1))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f102,f9])). 9.25/2.06 fof(f112,plain,( 9.25/2.06 ( ! [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), 9.25/2.06 inference(resolution,[],[f106,f96])). 9.25/2.06 fof(f114,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (is_a_theorem(implies(X0,implies(X1,X2))) | ~is_a_theorem(implies(X0,X2))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f106,f12])). 9.25/2.06 fof(f128,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (~is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) | is_a_theorem(X2)) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f114,f16])). 9.25/2.06 fof(f136,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2)))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f128,f96])). 9.25/2.06 fof(f144,plain,( 9.25/2.06 ( ! [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), 9.25/2.06 inference(resolution,[],[f128,f112])). 9.25/2.06 fof(f151,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (~is_a_theorem(implies(implies(X2,X0),X1)) | is_a_theorem(implies(X0,X1))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f136,f9])). 9.25/2.06 fof(f185,plain,( 9.25/2.06 ( ! [X2,X3,X0,X1] : (is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f144,f31])). 9.25/2.06 fof(f197,plain,( 9.25/2.06 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(n(X0),X1),X2),implies(X0,X2)))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f144,f32])). 9.25/2.06 fof(f199,plain,( 9.25/2.06 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(n(X0),X0),X1)))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f144,f83])). 9.25/2.06 fof(f216,plain,( 9.25/2.06 ( ! [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), 9.25/2.06 inference(resolution,[],[f185,f9])). 9.25/2.06 fof(f221,plain,( 9.25/2.06 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(X0,implies(implies(n(X1),X3),X2))) | is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f197,f106])). 9.25/2.06 fof(f233,plain,( 9.25/2.06 ( ! [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), 9.25/2.06 inference(resolution,[],[f216,f102])). 9.25/2.06 fof(f323,plain,( 9.25/2.06 ( ! [X0,X1] : (is_a_theorem(implies(implies(implies(implies(n(X0),X0),X0),X1),X1))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f151,f31])). 9.25/2.06 fof(f365,plain,( 9.25/2.06 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,implies(n(X1),X1)),implies(X0,X1)))) ) | ~spl0_2), 9.25/2.06 inference(resolution,[],[f323,f216])). 9.25/2.07 fof(f376,plain,( 9.25/2.07 ( ! [X0,X1] : (is_a_theorem(implies(implies(n(X0),X1),implies(implies(X1,X0),X0)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f365,f216])). 9.25/2.07 fof(f384,plain,( 9.25/2.07 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(implies(X0,X1),X1)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f376,f151])). 9.25/2.07 fof(f388,plain,( 9.25/2.07 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,X1),X1)) | ~is_a_theorem(implies(n(X1),X0))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f376,f9])). 9.25/2.07 fof(f425,plain,( 9.25/2.07 ( ! [X0,X1] : (is_a_theorem(implies(n(X0),implies(X0,X1)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f384,f221])). 9.25/2.07 fof(f441,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (~is_a_theorem(implies(n(implies(X0,X1)),implies(X2,X1))) | is_a_theorem(implies(implies(X0,X2),implies(X0,X1)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f388,f216])). 9.25/2.07 fof(f554,plain,( 9.25/2.07 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f441,f425])). 9.25/2.07 fof(f593,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X0,implies(X1,implies(X1,X2)))) | is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f554,f106])). 9.25/2.07 fof(f614,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(X0,X2))) | ~is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f593,f233])). 9.25/2.07 fof(f638,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X0,implies(X1,X2))) | is_a_theorem(implies(X1,implies(X0,X2)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f614,f151])). 9.25/2.07 fof(f752,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f638,f96])). 9.25/2.07 fof(f753,plain,( 9.25/2.07 ( ! [X0,X1] : (is_a_theorem(implies(implies(n(X0),X0),implies(implies(X0,X1),X1)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f638,f199])). 9.25/2.07 fof(f809,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(X0,X2))) | ~is_a_theorem(implies(X1,X2))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f752,f9])). 9.25/2.07 fof(f827,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (~is_a_theorem(implies(X0,implies(n(X1),X1))) | is_a_theorem(implies(X0,implies(implies(X1,X2),X2)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f753,f106])). 9.25/2.07 fof(f837,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X1,X0),implies(X1,X2))) | ~is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f809,f593])). 9.25/2.07 fof(f853,plain,( 9.25/2.07 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),X3))) | is_a_theorem(implies(implies(X0,X2),implies(implies(X2,X1),X3)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f837,f216])). 9.25/2.07 fof(f908,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (~is_a_theorem(implies(n(X1),X0)) | is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),X2)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f827,f102])). 9.25/2.07 fof(f959,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(X0,X1),X0),implies(implies(X0,X2),X2)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f908,f425])). 9.25/2.07 fof(f984,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X0),X1)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f959,f638])). 9.25/2.07 fof(f991,plain,( 9.25/2.07 ( ! [X2,X0,X1] : (is_a_theorem(implies(implies(implies(X0,X1),X0),implies(X2,X0)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f984,f128])). 9.25/2.07 fof(f1063,plain,( 9.25/2.07 ( ! [X2,X3,X0,X1] : (~is_a_theorem(implies(X0,implies(implies(X2,X3),X2))) | is_a_theorem(implies(X0,implies(X1,X2)))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f991,f106])). 9.25/2.07 fof(f1121,plain,( 9.25/2.07 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,n(X0)),implies(X1,n(X0))))) ) | ~spl0_2), 9.25/2.07 inference(resolution,[],[f1063,f199])). 9.25/2.07 fof(f1152,plain,( 9.25/2.07 $false | ~spl0_2), 9.25/2.07 inference(unit_resulting_resolution,[],[f853,f10,f1121])). 9.25/2.07 fof(f1169,plain,( 9.25/2.07 ~spl0_2), 9.25/2.07 inference(avatar_contradiction_clause,[],[f1152])). 9.25/2.07 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f26])). 9.25/2.07 cnf(s9, plain, ~spl0_1, inference(sat_conversion,[],[f67])). 9.25/2.07 cnf(s25, plain, ~spl0_2, inference(sat_conversion,[],[f1169])). 9.25/2.07 cnf(s26, plain, $false, inference(rat,[],[s1,s25,s9])). 9.25/2.07 fof(f1170,plain,( 9.25/2.07 $false), 9.25/2.07 inference(avatar_sat_refutation,[],[s26])). 9.25/2.07 % SZS output end Proof for theBenchmark 9.25/2.07 % (2903574)------------------------------ 9.25/2.07 % (2903574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200) 9.25/2.07 % (2903574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 9.25/2.07 % (2903574)CaDiCaL version: 2.1.3 9.25/2.07 % (2903574)Termination reason: Refutation 9.25/2.07 % (2903574)Time elapsed: 0.876 s 9.25/2.07 % (2903574)Peak memory usage: 132 MB 9.25/2.07 % (2903574)Instructions burned: 1327 (million) 9.25/2.07 % (2903574)------------------------------ 9.25/2.07 % (2903574)------------------------------ 9.25/2.07 % (2903568)Success in time 1.257 s 9.25/2.07 % Vampire exiting 9.25/2.07 EOF