%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL043-3 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:37:43 AM UTC 2026
% Result : Unsatisfiable 5.47s 1.45s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 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,
! [X2,X0,X1] : apply(apply(apply(h,X0),X1),X2) = apply(apply(apply(X0,X1),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f6,plain,
! [X2,X3,X0,X1] : apply(apply(apply(h,apply(apply(b,X0),X1)),X2),X3) = apply(apply(apply(X0,apply(X1,X2)),X3),X2),
inference(superposition,[],[f2,f1]) ).
fof(f9,plain,
! [X2,X0,X1] : apply(apply(apply(h,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X1),
inference(superposition,[],[f2,f1]) ).
fof(f34,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X2),X1)) = apply(apply(apply(h,apply(b,apply(b,X0))),X1),X2),
inference(superposition,[],[f1,f9]) ).
fof(f78,plain,
! [X0] : apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f86,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,X0))),
inference(forward_demodulation,[],[f78,f1]) ).
fof(f88,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,X0))),h),
inference(forward_demodulation,[],[f86,f6]) ).
fof(f90,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,X0))),h),
inference(forward_demodulation,[],[f88,f1]) ).
fof(f151,plain,
! [X2,X0,X1] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(h,apply(apply(b,b),X0)),X1),X2),
inference(superposition,[],[f1,f6]) ).
fof(f312,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,X0))),apply(h,apply(b,apply(b,X0)))),
inference(superposition,[],[f90,f151]) ).
fof(f321,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,X0))),h),apply(h,apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f312,f6]) ).
fof(f333,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(h,apply(b,apply(b,X0))),apply(h,apply(b,apply(b,X0)))),apply(h,apply(b,apply(b,X0)))),
inference(superposition,[],[f321,f151]) ).
fof(f353,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(superposition,[],[f34,f333]) ).
fof(f413,plain,
apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
inference(superposition,[],[f4,f353]) ).
fof(f414,plain,
$false,
inference(trivial_inequality_removal,[],[f413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL043-3 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:33:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 5.47/1.45 % (95494)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.47/1.45 % (95500)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3979558774:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.47/1.45 % (95505)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4272885865:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.47/1.45 % (95499)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3620907192:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.47/1.45 % (95502)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1431424656:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.47/1.45 % (95503)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1981864087:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.47/1.45 % (95501)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=223705976:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.47/1.45 % (95504)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2395203155:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.47/1.45 % (95502)Instruction limit reached!
% 5.47/1.45 % (95502)------------------------------
% 5.47/1.45 % (95502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.45 % (95502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.45 % (95502)CaDiCaL version: 2.1.3
% 5.47/1.45 % (95502)Termination reason: Instruction limit
% 5.47/1.45 % (95502)Termination phase: Saturation
% 5.47/1.45 % (95502)Time elapsed: 0.082 s
% 5.47/1.45 % (95502)Peak memory usage: 89 MB
% 5.47/1.45 % (95502)Instructions burned: 137 (million)
% 5.47/1.45 % (95503)Instruction limit reached!
% 5.47/1.45 % (95503)------------------------------
% 5.47/1.45 % (95503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.45 % (95503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.45 % (95503)CaDiCaL version: 2.1.3
% 5.47/1.45 % (95503)Termination reason: Instruction limit
% 5.47/1.45 % (95503)Termination phase: Saturation
% 5.47/1.45 % (95503)Time elapsed: 0.097 s
% 5.47/1.45 % (95503)Peak memory usage: 89 MB
% 5.47/1.45 % (95503)Instructions burned: 184 (million)
% 5.47/1.45 % (95504)Instruction limit reached!
% 5.47/1.45 % (95504)------------------------------
% 5.47/1.45 % (95504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.45 % (95504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.45 % (95504)CaDiCaL version: 2.1.3
% 5.47/1.45 % (95504)Termination reason: Instruction limit
% 5.47/1.45 % (95504)Termination phase: Saturation
% 5.47/1.45 % (95504)Time elapsed: 0.164 s
% 5.47/1.45 % (95504)Peak memory usage: 91 MB
% 5.47/1.45 % (95504)Instructions burned: 257 (million)
% 5.47/1.45 % (95513)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1788204994:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.47/1.45 % (95514)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=879567083:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.47/1.45 % (95515)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=743899316:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.47/1.45 % (95515)Refutation not found, incomplete strategy
% 5.47/1.45 % (95515)------------------------------
% 5.47/1.45 % (95515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.45 % (95515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.45 % (95515)CaDiCaL version: 2.1.3
% 5.47/1.45 % (95515)Termination reason: Refutation not found, incomplete strategy
% 5.47/1.45 % (95515)Time elapsed: 0.002 s
% 5.47/1.45 % (95515)Peak memory usage: 88 MB
% 5.47/1.45 % (95515)Instructions burned: 1 (million)
% 5.47/1.45 % (95500)First to succeed.
% 5.47/1.45 % (95500)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-95494"
% 5.47/1.45 % (95515)------------------------------
% 5.47/1.45 % (95515)------------------------------
% 5.47/1.45 % (95500)Refutation found. Thanks to Tanya!
% 5.47/1.45 % SZS status Unsatisfiable for theBenchmark
% 5.47/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 5.47/1.45 % (95500)------------------------------
% 5.47/1.45 % (95500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.45 % (95500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.45 % (95500)CaDiCaL version: 2.1.3
% 5.47/1.45 % (95500)Termination reason: Refutation
% 5.47/1.45 % (95500)Time elapsed: 0.424 s
% 5.47/1.45 % (95500)Peak memory usage: 130 MB
% 5.47/1.45 % (95500)Instructions burned: 1088 (million)
% 5.47/1.45 % (95500)------------------------------
% 5.47/1.45 % (95500)------------------------------
% 5.47/1.45 % (95494)Success in time 0.698 s
% 5.47/1.45 % Vampire exiting
%------------------------------------------------------------------------------