%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL003-6 : 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 : n020.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 7.66s 2.05s
% Output : Refutation 7.66s
% 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 : 10 ( 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(apply(b,apply(w,w)),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(apply(b,apply(w,w)),w)),b)),b),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),w)),b)),b),fixed_pt)),
inference(resolution,[],[f3,f4]) ).
fof(f12,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),b),apply(b,fixed_pt)) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),b),apply(b,fixed_pt))),
inference(forward_demodulation,[],[f11,f1]) ).
fof(f13,plain,
apply(apply(apply(b,apply(w,w)),w),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),w),apply(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(f28,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f52,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,f28]) ).
fof(f1216,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,[],[f52,f8]) ).
fof(f1315,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,f1216]) ).
fof(f1316,plain,
$false,
inference(trivial_inequality_removal,[],[f1315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL003-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n020.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Mon Sep 28 21:30:05 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.30 Running first-order theorem proving
% 0.11/0.30 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
% 7.66/2.05 % (585722)Input is clausal, will run a generic CNF schedule.
% 7.66/2.05 % (585746)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3080353098:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.66/2.05 % (585745)lrs+10_1_sil=8000:sp=occurrence:random_seed=2680581338:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.66/2.05 % (585746)Instruction limit reached!
% 7.66/2.05 % (585746)------------------------------
% 7.66/2.05 % (585746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585746)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585746)Termination reason: Instruction limit
% 7.66/2.05 % (585746)Termination phase: Saturation
% 7.66/2.05 % (585746)Time elapsed: 0.048 s
% 7.66/2.05 % (585746)Peak memory usage: 88 MB
% 7.66/2.05 % (585746)Instructions burned: 114 (million)
% 7.66/2.05 % (585742)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=3421489356:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.66/2.05 % (585745)Instruction limit reached!
% 7.66/2.05 % (585745)------------------------------
% 7.66/2.05 % (585745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585745)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585745)Termination reason: Instruction limit
% 7.66/2.05 % (585745)Termination phase: Saturation
% 7.66/2.05 % (585745)Time elapsed: 0.072 s
% 7.66/2.05 % (585745)Peak memory usage: 89 MB
% 7.66/2.05 % (585745)Instructions burned: 109 (million)
% 7.66/2.05 % (585743)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1480659914:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.66/2.05 % (585744)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=832534046:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.66/2.05 % (585747)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1754088676:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.66/2.05 % (585748)dis-21_1_sil=8000:lcm=predicate:random_seed=2518229365: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)
% 7.66/2.05 % (585748)Refutation not found, incomplete strategy
% 7.66/2.05 % (585748)------------------------------
% 7.66/2.05 % (585748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585748)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585748)Termination reason: Refutation not found, incomplete strategy
% 7.66/2.05 % (585748)Time elapsed: 0.002 s
% 7.66/2.05 % (585748)Peak memory usage: 88 MB
% 7.66/2.05 % (585758)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2305427572: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)
% 7.66/2.05 % (585758)Refutation not found, incomplete strategy
% 7.66/2.05 % (585758)------------------------------
% 7.66/2.05 % (585758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585758)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585758)Termination reason: Refutation not found, incomplete strategy
% 7.66/2.05 % (585758)Time elapsed: 0.001 s
% 7.66/2.05 % (585758)Peak memory usage: 88 MB
% 7.66/2.05 % (585758)Instructions burned: 1 (million)
% 7.66/2.05 % (585747)Instruction limit reached!
% 7.66/2.05 % (585747)------------------------------
% 7.66/2.05 % (585747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585747)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585747)Termination reason: Instruction limit
% 7.66/2.05 % (585747)Termination phase: Saturation
% 7.66/2.05 % (585747)Time elapsed: 0.140 s
% 7.66/2.05 % (585747)Peak memory usage: 89 MB
% 7.66/2.05 % (585747)Instructions burned: 181 (million)
% 7.66/2.05 % (585754)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=975578088:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 7.66/2.05 % (585754)Refutation not found, incomplete strategy
% 7.66/2.05 % (585754)------------------------------
% 7.66/2.05 % (585754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585754)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585754)Termination reason: Refutation not found, incomplete strategy
% 7.66/2.05 % (585754)Time elapsed: 0.002 s
% 7.66/2.05 % (585754)Peak memory usage: 88 MB
% 7.66/2.05 % (585758)------------------------------
% 7.66/2.05 % (585758)------------------------------
% 7.66/2.05 % (585764)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3997975827:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 7.66/2.05 % (585764)Refutation not found, incomplete strategy
% 7.66/2.05 % (585764)------------------------------
% 7.66/2.05 % (585764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585764)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585764)Termination reason: Refutation not found, incomplete strategy
% 7.66/2.05 % (585764)Time elapsed: 0.002 s
% 7.66/2.05 % (585764)Peak memory usage: 88 MB
% 7.66/2.05 % (585748)------------------------------
% 7.66/2.05 % (585748)------------------------------
% 7.66/2.05 % (585768)lrs+10_64_to=lpo:sil=8000:random_seed=3213519113:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 7.66/2.05 % (585768)Instruction limit reached!
% 7.66/2.05 % (585768)------------------------------
% 7.66/2.05 % (585768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585768)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585768)Termination reason: Instruction limit
% 7.66/2.05 % (585768)Termination phase: Saturation
% 7.66/2.05 % (585768)Time elapsed: 0.044 s
% 7.66/2.05 % (585768)Peak memory usage: 89 MB
% 7.66/2.05 % (585768)Instructions burned: 128 (million)
% 7.66/2.05 % (585754)------------------------------
% 7.66/2.05 % (585754)------------------------------
% 7.66/2.05 % (585770)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1115157230:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 7.66/2.05 % (585770)First to succeed.
% 7.66/2.05 % (585770)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-585722"
% 7.66/2.05 % (585764)------------------------------
% 7.66/2.05 % (585764)------------------------------
% 7.66/2.05 % (585773)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=991056968:i=3394:sd=4:ss=included:sgt=64_2992 on theBenchmark for (2992ds/3394Mi)
% 7.66/2.05 % (585772)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1727190652:i=157:gtg=all_2992 on theBenchmark for (2992ds/157Mi)
% 7.66/2.05 % (585772)Instruction limit reached!
% 7.66/2.05 % (585772)------------------------------
% 7.66/2.05 % (585772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585772)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585772)Termination reason: Instruction limit
% 7.66/2.05 % (585772)Termination phase: Saturation
% 7.66/2.05 % (585772)Time elapsed: 0.103 s
% 7.66/2.05 % (585772)Peak memory usage: 91 MB
% 7.66/2.05 % (585772)Instructions burned: 157 (million)
% 7.66/2.05 % (585770)Refutation found. Thanks to Tanya!
% 7.66/2.05 % SZS status Unsatisfiable for theBenchmark
% 7.66/2.05 % SZS output start Proof for theBenchmark
% See solution above
% 7.66/2.05 % (585770)------------------------------
% 7.66/2.05 % (585770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.66/2.05 % (585770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/2.05 % (585770)CaDiCaL version: 2.1.3
% 7.66/2.05 % (585770)Termination reason: Refutation
% 7.66/2.05 % (585770)Time elapsed: 0.049 s
% 7.66/2.05 % (585770)Peak memory usage: 90 MB
% 7.66/2.05 % (585770)Instructions burned: 140 (million)
% 7.66/2.05 % (585770)------------------------------
% 7.66/2.05 % (585770)------------------------------
% 7.66/2.05 % (585722)Success in time 0.96 s
% 7.66/2.05 % Vampire exiting
%------------------------------------------------------------------------------