%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL003-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 6.28s 1.48s
% Output : Refutation 6.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 19 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 9 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 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 : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
fof(f3,axiom,
! [X0] :
( apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt))
| fixed_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b))),
file('/export/starexec/sandbox/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(f9,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(w,b),b))),
inference(superposition,[],[f4,f2]) ).
fof(f10,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(w,w),b))),
inference(forward_demodulation,[],[f9,f2]) ).
fof(f35,plain,
! [X0] : apply(b,apply(b,X0)) = apply(apply(apply(w,w),b),X0),
inference(superposition,[],[f1,f8]) ).
fof(f38,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f41,plain,
! [X0,X1] :
( fixed_point(apply(apply(b,X0),X1))
| apply(X0,apply(X1,fixed_pt)) != apply(fixed_pt,apply(X0,apply(X1,fixed_pt))) ),
inference(superposition,[],[f3,f1]) ).
fof(f65,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,f38]) ).
fof(f439,plain,
apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(w,w),b),fixed_pt)) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(w,w),b),fixed_pt))),
inference(resolution,[],[f41,f10]) ).
fof(f453,plain,
apply(apply(w,w),apply(w,apply(apply(apply(w,w),b),fixed_pt))) != apply(fixed_pt,apply(apply(w,w),apply(w,apply(apply(apply(w,w),b),fixed_pt)))),
inference(forward_demodulation,[],[f439,f1]) ).
fof(f455,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,[],[f453,f35]) ).
fof(f1278,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,[],[f65,f8]) ).
fof(f1377,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,[],[f455,f1278]) ).
fof(f1378,plain,
$false,
inference(trivial_inequality_removal,[],[f1377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n017.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 21:24:36 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running first-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.28/1.48 % (4050434)Input is clausal, will run a generic CNF schedule.
% 6.28/1.48 % (4050492)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=371628330:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.28/1.48 % (4050489)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=1614275619:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.28/1.48 % (4050493)lrs+10_1_sil=8000:sp=occurrence:random_seed=2486174553:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.28/1.48 % (4050490)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2833250120:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.28/1.48 % (4050498)dis-21_1_sil=8000:lcm=predicate:random_seed=1247611316:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 6.28/1.48 % (4050494)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3286041814:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.28/1.48 % (4050498)Refutation not found, incomplete strategy
% 6.28/1.48 % (4050498)------------------------------
% 6.28/1.48 % (4050498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050498)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050498)Termination reason: Refutation not found, incomplete strategy
% 6.28/1.48 % (4050498)Time elapsed: 0.001 s
% 6.28/1.48 % (4050498)Peak memory usage: 88 MB
% 6.28/1.48 % (4050496)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1515305559:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.28/1.48 % (4050494)Instruction limit reached!
% 6.28/1.48 % (4050494)------------------------------
% 6.28/1.48 % (4050494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050494)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050494)Termination reason: Instruction limit
% 6.28/1.48 % (4050494)Termination phase: Saturation
% 6.28/1.48 % (4050494)Time elapsed: 0.069 s
% 6.28/1.48 % (4050494)Peak memory usage: 88 MB
% 6.28/1.48 % (4050494)Instructions burned: 116 (million)
% 6.28/1.48 % (4050493)Instruction limit reached!
% 6.28/1.48 % (4050493)------------------------------
% 6.28/1.48 % (4050493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050493)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050493)Termination reason: Instruction limit
% 6.28/1.48 % (4050493)Termination phase: Saturation
% 6.28/1.48 % (4050493)Time elapsed: 0.069 s
% 6.28/1.48 % (4050493)Peak memory usage: 89 MB
% 6.28/1.48 % (4050493)Instructions burned: 107 (million)
% 6.28/1.48 % (4050496)Instruction limit reached!
% 6.28/1.48 % (4050496)------------------------------
% 6.28/1.48 % (4050496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050496)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050496)Termination reason: Instruction limit
% 6.28/1.48 % (4050496)Termination phase: Saturation
% 6.28/1.48 % (4050496)Time elapsed: 0.071 s
% 6.28/1.48 % (4050496)Peak memory usage: 89 MB
% 6.28/1.48 % (4050496)Instructions burned: 184 (million)
% 6.28/1.48 % (4050601)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2527708654:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.28/1.48 % (4050601)Refutation not found, incomplete strategy
% 6.28/1.48 % (4050601)------------------------------
% 6.28/1.48 % (4050601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050601)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050601)Termination reason: Refutation not found, incomplete strategy
% 6.28/1.48 % (4050601)Time elapsed: 0.001 s
% 6.28/1.48 % (4050601)Peak memory usage: 88 MB
% 6.28/1.48 % (4050583)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=3784614130:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.28/1.48 % (4050585)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2631070430:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 6.28/1.48 % (4050583)Refutation not found, incomplete strategy
% 6.28/1.48 % (4050583)------------------------------
% 6.28/1.48 % (4050583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050583)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050583)Termination reason: Refutation not found, incomplete strategy
% 6.28/1.48 % (4050583)Time elapsed: 0.001 s
% 6.28/1.48 % (4050583)Peak memory usage: 88 MB
% 6.28/1.48 % (4050585)Refutation not found, incomplete strategy
% 6.28/1.48 % (4050585)------------------------------
% 6.28/1.48 % (4050585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050585)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050585)Termination reason: Refutation not found, incomplete strategy
% 6.28/1.48 % (4050585)Time elapsed: 0.001 s
% 6.28/1.48 % (4050585)Peak memory usage: 88 MB
% 6.28/1.48 % (4050585)Instructions burned: 1 (million)
% 6.28/1.48 % (4050498)------------------------------
% 6.28/1.48 % (4050498)------------------------------
% 6.28/1.48 % (4050601)------------------------------
% 6.28/1.48 % (4050601)------------------------------
% 6.28/1.48 % (4050611)lrs+10_64_to=lpo:sil=8000:random_seed=1527500797:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.28/1.48 % (4050585)------------------------------
% 6.28/1.48 % (4050585)------------------------------
% 6.28/1.48 % (4050583)------------------------------
% 6.28/1.48 % (4050583)------------------------------
% 6.28/1.48 % (4050612)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2113388554:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 6.28/1.48 % (4050611)Instruction limit reached!
% 6.28/1.48 % (4050611)------------------------------
% 6.28/1.48 % (4050611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050611)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050611)Termination reason: Instruction limit
% 6.28/1.48 % (4050611)Termination phase: Saturation
% 6.28/1.48 % (4050611)Time elapsed: 0.084 s
% 6.28/1.48 % (4050611)Peak memory usage: 89 MB
% 6.28/1.48 % (4050611)Instructions burned: 127 (million)
% 6.28/1.48 % (4050612)First to succeed.
% 6.28/1.48 % (4050612)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4050434"
% 6.28/1.48 % (4050614)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1959028239:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.28/1.48 % (4050615)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2550509737:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.28/1.48 % (4050490)Also succeeded, but the first one will report.
% 6.28/1.48 % (4050489)Also succeeded, but the first one will report.
% 6.28/1.48 % (4050617)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=2258103391:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 6.28/1.48 % (4050492)Also succeeded, but the first one will report.
% 6.28/1.48 % (4050612)Refutation found. Thanks to Tanya!
% 6.28/1.48 % SZS status Unsatisfiable for theBenchmark
% 6.28/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 6.28/1.48 % (4050612)------------------------------
% 6.28/1.48 % (4050612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.28/1.48 % (4050612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.28/1.48 % (4050612)CaDiCaL version: 2.1.3
% 6.28/1.48 % (4050612)Termination reason: Refutation
% 6.28/1.48 % (4050612)Time elapsed: 0.051 s
% 6.28/1.48 % (4050612)Peak memory usage: 90 MB
% 6.28/1.48 % (4050612)Instructions burned: 138 (million)
% 6.28/1.48 % (4050612)------------------------------
% 6.28/1.48 % (4050612)------------------------------
% 6.28/1.48 % (4050434)Success in time 0.846 s
% 6.28/1.48 % Vampire exiting
%------------------------------------------------------------------------------