%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL042-9 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:37:42 AM UTC 2026
% Result : Unsatisfiable 7.60s 1.85s
% Output : Refutation 7.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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 : 21 ( 21 !; 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(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f12,plain,
! [X2,X0,X1] : apply(apply(w1,X2),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f2,f1]) ).
fof(f27,plain,
! [X2,X0,X1] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),X2)) = apply(X1,apply(apply(X2,X0),X0)),
inference(superposition,[],[f1,f12]) ).
fof(f45,plain,
! [X2,X0,X1] : apply(X2,apply(apply(w1,X0),X1)) = apply(apply(w1,X0),apply(apply(b,apply(b,X2)),X1)),
inference(superposition,[],[f27,f2]) ).
fof(f93,plain,
! [X0] : apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f100,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),X0))),
inference(forward_demodulation,[],[f93,f1]) ).
fof(f103,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,apply(apply(apply(apply(b,b),b),X0),w1)),w1),
inference(forward_demodulation,[],[f100,f12]) ).
fof(f105,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1),
inference(forward_demodulation,[],[f103,f1]) ).
fof(f125,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),X1)),
inference(superposition,[],[f2,f45]) ).
fof(f152,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(superposition,[],[f125,f105]) ).
fof(f208,plain,
apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
inference(superposition,[],[f4,f152]) ).
fof(f209,plain,
$false,
inference(trivial_inequality_removal,[],[f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL042-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n012.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:30:04 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 7.60/1.85 % (3800108)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.60/1.85 % (3800116)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2723568095:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.60/1.85 % (3800114)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=2332026789:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.60/1.85 % (3800113)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=145119225:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.60/1.85 % (3800115)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=631098809:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.60/1.85 % (3800117)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4112218394:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.60/1.85 % (3800118)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1553008752:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.60/1.85 % (3800119)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3458310305:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.60/1.85 % (3800116)Instruction limit reached!
% 7.60/1.85 % (3800116)------------------------------
% 7.60/1.85 % (3800116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/1.85 % (3800116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/1.85 % (3800116)CaDiCaL version: 2.1.3
% 7.60/1.85 % (3800116)Termination reason: Instruction limit
% 7.60/1.85 % (3800116)Termination phase: Saturation
% 7.60/1.85 % (3800116)Time elapsed: 0.074 s
% 7.60/1.85 % (3800116)Peak memory usage: 89 MB
% 7.60/1.85 % (3800116)Instructions burned: 138 (million)
% 7.60/1.85 % (3800117)Instruction limit reached!
% 7.60/1.85 % (3800117)------------------------------
% 7.60/1.85 % (3800117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/1.85 % (3800117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/1.85 % (3800117)CaDiCaL version: 2.1.3
% 7.60/1.85 % (3800117)Termination reason: Instruction limit
% 7.60/1.85 % (3800117)Termination phase: Saturation
% 7.60/1.85 % (3800117)Time elapsed: 0.089 s
% 7.60/1.85 % (3800117)Peak memory usage: 89 MB
% 7.60/1.85 % (3800117)Instructions burned: 181 (million)
% 7.60/1.85 % (3800118)Instruction limit reached!
% 7.60/1.85 % (3800118)------------------------------
% 7.60/1.85 % (3800118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/1.85 % (3800118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/1.85 % (3800118)CaDiCaL version: 2.1.3
% 7.60/1.85 % (3800118)Termination reason: Instruction limit
% 7.60/1.85 % (3800118)Termination phase: Saturation
% 7.60/1.85 % (3800118)Time elapsed: 0.146 s
% 7.60/1.85 % (3800118)Peak memory usage: 91 MB
% 7.60/1.85 % (3800118)Instructions burned: 257 (million)
% 7.60/1.85 % (3800127)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3922464268:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 7.60/1.85 % (3800128)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=479118901:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 7.60/1.85 % (3800129)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=707143312:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 7.60/1.85 % (3800129)Refutation not found, incomplete strategy
% 7.60/1.85 % (3800129)------------------------------
% 7.60/1.85 % (3800129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/1.85 % (3800129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/1.85 % (3800129)CaDiCaL version: 2.1.3
% 7.60/1.85 % (3800129)Termination reason: Refutation not found, incomplete strategy
% 7.60/1.85 % (3800129)Time elapsed: 0.001 s
% 7.60/1.85 % (3800129)Peak memory usage: 87 MB
% 7.60/1.85 % (3800129)Instructions burned: 1 (million)
% 7.60/1.85 % (3800129)------------------------------
% 7.60/1.85 % (3800129)------------------------------
% 7.60/1.85 % (3800114)First to succeed.
% 7.60/1.85 % (3800114)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3800108"
% 7.60/1.85 % (3800119)Instruction limit reached!
% 7.60/1.85 % (3800119)------------------------------
% 7.60/1.85 % (3800119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/1.85 % (3800119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/1.85 % (3800119)CaDiCaL version: 2.1.3
% 7.60/1.85 % (3800119)Termination reason: Instruction limit
% 7.60/1.85 % (3800119)Termination phase: Saturation
% 7.60/1.85 % (3800119)Time elapsed: 0.572 s
% 7.60/1.85 % (3800119)Peak memory usage: 95 MB
% 7.60/1.85 % (3800119)Instructions burned: 1187 (million)
% 7.60/1.85 % (3800133)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3688891253:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 7.60/1.85 % (3800113)Also succeeded, but the first one will report.
% 7.60/1.85 % (3800134)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=1816665833:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 7.60/1.85 % (3800127)Also succeeded, but the first one will report.
% 7.60/1.85 % (3800128)Also succeeded, but the first one will report.
% 7.60/1.85 % (3800114)Refutation found. Thanks to Tanya!
% 7.60/1.85 % SZS status Unsatisfiable for theBenchmark
% 7.60/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 7.60/1.85 % (3800114)------------------------------
% 7.60/1.85 % (3800114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/1.85 % (3800114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/1.85 % (3800114)CaDiCaL version: 2.1.3
% 7.60/1.85 % (3800114)Termination reason: Refutation
% 7.60/1.85 % (3800114)Time elapsed: 0.570 s
% 7.60/1.85 % (3800114)Peak memory usage: 127 MB
% 7.60/1.85 % (3800114)Instructions burned: 965 (million)
% 7.60/1.85 % (3800114)------------------------------
% 7.60/1.85 % (3800114)------------------------------
% 7.60/1.85 % (3800108)Success in time 1.006 s
% 7.60/1.85 % Vampire exiting
%------------------------------------------------------------------------------