%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL003-2 : 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 : n008.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 8.50s 2.07s
% Output : Refutation 8.50s
% 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(w,w)),apply(apply(b,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(w,w)),apply(apply(b,w),apply(apply(w,b),b)))),
inference(superposition,[],[f4,f2]) ).
fof(f10,plain,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,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(w,w),apply(apply(apply(b,w),apply(apply(w,w),b)),fixed_pt)) != apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),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(f1271,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(f1370,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,f1271]) ).
fof(f1371,plain,
$false,
inference(trivial_inequality_removal,[],[f1370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:29:54 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 8.50/2.06 % (2671927)Input is clausal, will run a generic CNF schedule.
% 8.50/2.06 % (2671996)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2820084183:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.50/2.06 % (2671993)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1050177473:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.50/2.06 % (2671992)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=2517730932:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.50/2.06 % (2671994)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=103219324:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.50/2.06 % (2671995)lrs+10_1_sil=8000:sp=occurrence:random_seed=69444875:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.50/2.06 % (2671997)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3960546489:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.50/2.06 % (2671996)Instruction limit reached!
% 8.50/2.06 % (2671996)------------------------------
% 8.50/2.06 % (2671996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.06 % (2671996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.06 % (2671996)CaDiCaL version: 2.1.3
% 8.50/2.06 % (2671996)Termination reason: Instruction limit
% 8.50/2.06 % (2671996)Termination phase: Saturation
% 8.50/2.06 % (2671996)Time elapsed: 0.038 s
% 8.50/2.06 % (2671996)Peak memory usage: 88 MB
% 8.50/2.06 % (2671996)Instructions burned: 116 (million)
% 8.50/2.06 % (2671998)dis-21_1_sil=8000:lcm=predicate:random_seed=2965268722: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)
% 8.50/2.06 % (2671998)Refutation not found, incomplete strategy
% 8.50/2.06 % (2671998)------------------------------
% 8.50/2.06 % (2671998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.06 % (2671998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.06 % (2671998)CaDiCaL version: 2.1.3
% 8.50/2.06 % (2671998)Termination reason: Refutation not found, incomplete strategy
% 8.50/2.06 % (2671998)Time elapsed: 0.001 s
% 8.50/2.06 % (2671998)Peak memory usage: 88 MB
% 8.50/2.06 % (2671995)Instruction limit reached!
% 8.50/2.06 % (2671995)------------------------------
% 8.50/2.06 % (2671995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.06 % (2671995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.06 % (2671995)CaDiCaL version: 2.1.3
% 8.50/2.06 % (2671995)Termination reason: Instruction limit
% 8.50/2.06 % (2671995)Termination phase: Saturation
% 8.50/2.06 % (2671995)Time elapsed: 0.070 s
% 8.50/2.06 % (2671995)Peak memory usage: 89 MB
% 8.50/2.06 % (2671995)Instructions burned: 108 (million)
% 8.50/2.06 % (2671997)Instruction limit reached!
% 8.50/2.06 % (2671997)------------------------------
% 8.50/2.06 % (2671997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.06 % (2671997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.07 % (2671997)CaDiCaL version: 2.1.3
% 8.50/2.07 % (2671997)Termination reason: Instruction limit
% 8.50/2.07 % (2671997)Termination phase: Saturation
% 8.50/2.07 % (2671997)Time elapsed: 0.105 s
% 8.50/2.07 % (2671997)Peak memory usage: 89 MB
% 8.50/2.07 % (2671997)Instructions burned: 182 (million)
% 8.50/2.07 % (2672045)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=1649618709:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 8.50/2.07 % (2672045)Refutation not found, incomplete strategy
% 8.50/2.07 % (2672045)------------------------------
% 8.50/2.07 % (2672045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.07 % (2672045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.07 % (2672045)CaDiCaL version: 2.1.3
% 8.50/2.07 % (2672045)Termination reason: Refutation not found, incomplete strategy
% 8.50/2.07 % (2672045)Time elapsed: 0.001 s
% 8.50/2.07 % (2672045)Peak memory usage: 88 MB
% 8.50/2.07 % (2672058)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3004444141: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)
% 8.50/2.07 % (2672058)Refutation not found, incomplete strategy
% 8.50/2.07 % (2672058)------------------------------
% 8.50/2.07 % (2672058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.07 % (2672058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.07 % (2672058)CaDiCaL version: 2.1.3
% 8.50/2.07 % (2672058)Termination reason: Refutation not found, incomplete strategy
% 8.50/2.07 % (2672058)Time elapsed: 0.003 s
% 8.50/2.07 % (2672058)Peak memory usage: 88 MB
% 8.50/2.07 % (2672058)Instructions burned: 1 (million)
% 8.50/2.07 % (2671998)------------------------------
% 8.50/2.07 % (2671998)------------------------------
% 8.50/2.07 % (2672069)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3909874162:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 8.50/2.07 % (2672069)Refutation not found, incomplete strategy
% 8.50/2.07 % (2672069)------------------------------
% 8.50/2.07 % (2672069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.07 % (2672069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.07 % (2672069)CaDiCaL version: 2.1.3
% 8.50/2.07 % (2672069)Termination reason: Refutation not found, incomplete strategy
% 8.50/2.07 % (2672069)Time elapsed: 0.002 s
% 8.50/2.07 % (2672069)Peak memory usage: 88 MB
% 8.50/2.07 % (2672045)------------------------------
% 8.50/2.07 % (2672045)------------------------------
% 8.50/2.07 % (2672105)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=468162403:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 8.50/2.07 % (2672103)lrs+10_64_to=lpo:sil=8000:random_seed=2377453342:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 8.50/2.07 % (2672058)------------------------------
% 8.50/2.07 % (2672058)------------------------------
% 8.50/2.07 % (2672105)First to succeed.
% 8.50/2.07 % (2672105)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2671927"
% 8.50/2.07 % (2672069)------------------------------
% 8.50/2.07 % (2672069)------------------------------
% 8.50/2.07 % (2672103)Instruction limit reached!
% 8.50/2.07 % (2672103)------------------------------
% 8.50/2.07 % (2672103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.07 % (2672103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.07 % (2672103)CaDiCaL version: 2.1.3
% 8.50/2.07 % (2672103)Termination reason: Instruction limit
% 8.50/2.07 % (2672103)Termination phase: Saturation
% 8.50/2.07 % (2672103)Time elapsed: 0.136 s
% 8.50/2.07 % (2672103)Peak memory usage: 89 MB
% 8.50/2.07 % (2672103)Instructions burned: 126 (million)
% 8.50/2.07 % (2671993)Also succeeded, but the first one will report.
% 8.50/2.07 % (2672105)Refutation found. Thanks to Tanya!
% 8.50/2.07 % SZS status Unsatisfiable for theBenchmark
% 8.50/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 8.50/2.07 % (2672105)------------------------------
% 8.50/2.07 % (2672105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.07 % (2672105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.07 % (2672105)CaDiCaL version: 2.1.3
% 8.50/2.07 % (2672105)Termination reason: Refutation
% 8.50/2.07 % (2672105)Time elapsed: 0.083 s
% 8.50/2.07 % (2672105)Peak memory usage: 90 MB
% 8.50/2.07 % (2672105)Instructions burned: 138 (million)
% 8.50/2.07 % (2672105)------------------------------
% 8.50/2.07 % (2672105)------------------------------
% 8.50/2.07 % (2671927)Success in time 1.108 s
% 8.50/2.07 % Vampire exiting
%------------------------------------------------------------------------------