%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL003-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:37:35 AM UTC 2026
% Result : Unsatisfiable 7.87s 1.89s
% Output : Refutation 7.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 13 unt; 0 def)
% Number of atoms : 15 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 7 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
fof(f3,axiom,
! [X0] :
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f8,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f11,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt)),
inference(resolution,[],[f3,f4]) ).
fof(f12,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt))),
inference(forward_demodulation,[],[f11,f1]) ).
fof(f13,plain,
apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))),
inference(forward_demodulation,[],[f12,f1]) ).
fof(f14,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[],[f13,f1]) ).
fof(f27,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f51,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2),
inference(superposition,[],[f1,f27]) ).
fof(f1061,plain,
! [X0] : apply(apply(w,w),apply(w,apply(b,apply(b,X0)))) = apply(X0,apply(apply(w,w),apply(w,apply(b,apply(b,X0))))),
inference(superposition,[],[f51,f8]) ).
fof(f1151,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))),
inference(backward_demodulation,[],[f14,f1061]) ).
fof(f1152,plain,
$false,
inference(trivial_inequality_removal,[],[f1151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n004.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Mon Sep 28 21:29:07 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running first-order theorem proving
% 0.25/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.87/1.89 % (804625)Input is clausal, will run a generic CNF schedule.
% 7.87/1.89 % (804643)dis-21_1_sil=8000:lcm=predicate:random_seed=1212146680:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 7.87/1.89 % (804643)Refutation not found, incomplete strategy
% 7.87/1.89 % (804643)------------------------------
% 7.87/1.89 % (804643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804643)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804643)Termination reason: Refutation not found, incomplete strategy
% 7.87/1.89 % (804643)Time elapsed: 0.001 s
% 7.87/1.89 % (804643)Peak memory usage: 88 MB
% 7.87/1.89 % (804638)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1658672866:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 7.87/1.89 % (804642)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3897547879:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 7.87/1.89 % (804639)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3202972833:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 7.87/1.89 % (804641)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3130993626:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 7.87/1.89 % (804640)lrs+10_1_sil=8000:sp=occurrence:random_seed=4050389875:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 7.87/1.89 % (804637)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=1815842167:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 7.87/1.89 % (804641)Instruction limit reached!
% 7.87/1.89 % (804641)------------------------------
% 7.87/1.89 % (804641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804641)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804641)Termination reason: Instruction limit
% 7.87/1.89 % (804641)Termination phase: Saturation
% 7.87/1.89 % (804641)Time elapsed: 0.094 s
% 7.87/1.89 % (804641)Peak memory usage: 88 MB
% 7.87/1.89 % (804641)Instructions burned: 114 (million)
% 7.87/1.89 % (804640)Instruction limit reached!
% 7.87/1.89 % (804640)------------------------------
% 7.87/1.89 % (804640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804640)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804640)Termination reason: Instruction limit
% 7.87/1.89 % (804640)Termination phase: Saturation
% 7.87/1.89 % (804640)Time elapsed: 0.095 s
% 7.87/1.89 % (804640)Peak memory usage: 89 MB
% 7.87/1.89 % (804640)Instructions burned: 108 (million)
% 7.87/1.89 % (804642)Instruction limit reached!
% 7.87/1.89 % (804642)------------------------------
% 7.87/1.89 % (804642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804642)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804642)Termination reason: Instruction limit
% 7.87/1.89 % (804642)Termination phase: Saturation
% 7.87/1.89 % (804642)Time elapsed: 0.158 s
% 7.87/1.89 % (804642)Peak memory usage: 89 MB
% 7.87/1.89 % (804642)Instructions burned: 181 (million)
% 7.87/1.89 % (804643)------------------------------
% 7.87/1.89 % (804643)------------------------------
% 7.87/1.89 % (804660)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3130267517:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 7.87/1.89 % (804657)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1849156750:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 7.87/1.89 % (804660)Refutation not found, incomplete strategy
% 7.87/1.89 % (804660)------------------------------
% 7.87/1.89 % (804660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804660)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804660)Termination reason: Refutation not found, incomplete strategy
% 7.87/1.89 % (804660)Time elapsed: 0.001 s
% 7.87/1.89 % (804660)Peak memory usage: 87 MB
% 7.87/1.89 % (804657)Refutation not found, incomplete strategy
% 7.87/1.89 % (804657)------------------------------
% 7.87/1.89 % (804657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804657)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804657)Termination reason: Refutation not found, incomplete strategy
% 7.87/1.89 % (804657)Time elapsed: 0.001 s
% 7.87/1.89 % (804657)Peak memory usage: 88 MB
% 7.87/1.89 % (804658)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=932697732:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 7.87/1.89 % (804658)Refutation not found, incomplete strategy
% 7.87/1.89 % (804658)------------------------------
% 7.87/1.89 % (804658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804658)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804658)Termination reason: Refutation not found, incomplete strategy
% 7.87/1.89 % (804658)Time elapsed: 0.002 s
% 7.87/1.89 % (804658)Peak memory usage: 88 MB
% 7.87/1.89 % (804658)Instructions burned: 1 (million)
% 7.87/1.89 % (804662)lrs+10_64_to=lpo:sil=8000:random_seed=648452052:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 7.87/1.89 % (804662)Instruction limit reached!
% 7.87/1.89 % (804662)------------------------------
% 7.87/1.89 % (804662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804662)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804662)Termination reason: Instruction limit
% 7.87/1.89 % (804662)Termination phase: Saturation
% 7.87/1.89 % (804662)Time elapsed: 0.128 s
% 7.87/1.89 % (804662)Peak memory usage: 89 MB
% 7.87/1.89 % (804662)Instructions burned: 126 (million)
% 7.87/1.89 % (804660)------------------------------
% 7.87/1.89 % (804660)------------------------------
% 7.87/1.89 % (804657)------------------------------
% 7.87/1.89 % (804657)------------------------------
% 7.87/1.89 % (804670)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=837680737:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 7.87/1.89 % (804658)------------------------------
% 7.87/1.89 % (804658)------------------------------
% 7.87/1.89 % (804670)First to succeed.
% 7.87/1.89 % (804670)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-804625"
% 7.87/1.89 % (804673)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2353818690:i=157:gtg=all_2992 on theBenchmark for (2992ds/157Mi)
% 7.87/1.89 % (804675)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=695143492:i=3394:sd=4:ss=included:sgt=64_2991 on theBenchmark for (2991ds/3394Mi)
% 7.87/1.89 % (804676)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=1423386168:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2991 on theBenchmark for (2991ds/106Mi)
% 7.87/1.89 % (804673)Instruction limit reached!
% 7.87/1.89 % (804673)------------------------------
% 7.87/1.89 % (804673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804673)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804673)Termination reason: Instruction limit
% 7.87/1.89 % (804673)Termination phase: Saturation
% 7.87/1.89 % (804673)Time elapsed: 0.105 s
% 7.87/1.89 % (804673)Peak memory usage: 91 MB
% 7.87/1.89 % (804673)Instructions burned: 157 (million)
% 7.87/1.89 % (804638)Also succeeded, but the first one will report.
% 7.87/1.89 % (804670)Refutation found. Thanks to Tanya!
% 7.87/1.89 % SZS status Unsatisfiable for theBenchmark
% 7.87/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 7.87/1.89 % (804670)------------------------------
% 7.87/1.89 % (804670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.87/1.89 % (804670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.89 % (804670)CaDiCaL version: 2.1.3
% 7.87/1.89 % (804670)Termination reason: Refutation
% 7.87/1.89 % (804670)Time elapsed: 0.045 s
% 7.87/1.89 % (804670)Peak memory usage: 90 MB
% 7.87/1.89 % (804670)Instructions burned: 125 (million)
% 7.87/1.89 % (804670)------------------------------
% 7.87/1.89 % (804670)------------------------------
% 7.87/1.89 % (804625)Success in time 1.035 s
% 7.87/1.89 % Vampire exiting
%------------------------------------------------------------------------------