%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL003-18 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:37:34 AM UTC 2026
% Result : Unsatisfiable 0.19s 1.90s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 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 : 6 ( 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 : 30 ( 30 !; 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,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,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(f7,plain,
! [X0,X1] : apply(apply(apply(w,X0),X1),X1) = apply(apply(w,apply(X0,X1)),X1),
inference(superposition,[],[f2,f2]) ).
fof(f8,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f9,plain,
! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(w,apply(X0,X1)),X1),
inference(forward_demodulation,[],[f7,f2]) ).
fof(f13,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f14,plain,
! [X2,X0,X1] : apply(apply(w,apply(apply(b,X0),X1)),X2) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f2,f1]) ).
fof(f15,plain,
! [X0] : apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f17,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),X0))),
inference(forward_demodulation,[],[f15,f1]) ).
fof(f18,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f17,f1]) ).
fof(f47,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,f13]) ).
fof(f55,plain,
! [X0,X1] : apply(X1,apply(apply(w,w),X0)) = apply(apply(apply(w,apply(b,apply(b,X1))),X0),X0),
inference(superposition,[],[f47,f8]) ).
fof(f95,plain,
! [X0,X1] : apply(X1,apply(apply(w,w),X0)) = apply(apply(w,apply(w,apply(b,apply(b,X1)))),X0),
inference(forward_demodulation,[],[f55,f2]) ).
fof(f241,plain,
! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(w,apply(apply(b,w),X0)),X1),
inference(superposition,[],[f14,f9]) ).
fof(f282,plain,
! [X0] : apply(apply(w,w),apply(apply(b,w),X0)) = apply(apply(w,apply(w,X0)),apply(apply(b,w),X0)),
inference(superposition,[],[f2,f241]) ).
fof(f307,plain,
! [X0] : apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(X0,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0))))),
inference(superposition,[],[f95,f282]) ).
fof(f315,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f307,f18]) ).
fof(f350,plain,
apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
inference(superposition,[],[f4,f315]) ).
fof(f351,plain,
$false,
inference(trivial_inequality_removal,[],[f350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-18 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:28:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 0.19/1.90 % (803617)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.19/1.90 % (803729)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=3880815027:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.19/1.90 % (803732)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2181115009:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.19/1.90 % (803730)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=2475910900:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.19/1.90 % (803731)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=392155892:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.19/1.90 % (803736)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3337100758:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.19/1.90 % (803734)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2633758403:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.19/1.90 % (803737)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2284204647:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.19/1.90 % (803732)Instruction limit reached!
% 0.19/1.90 % (803732)------------------------------
% 0.19/1.90 % (803732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.90 % (803732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.90 % (803732)CaDiCaL version: 2.1.3
% 0.19/1.90 % (803732)Termination reason: Instruction limit
% 0.19/1.90 % (803732)Termination phase: Saturation
% 0.19/1.90 % (803732)Time elapsed: 0.134 s
% 0.19/1.90 % (803732)Peak memory usage: 88 MB
% 0.19/1.90 % (803732)Instructions burned: 136 (million)
% 0.19/1.90 % (803734)Instruction limit reached!
% 0.19/1.90 % (803734)------------------------------
% 0.19/1.90 % (803734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.90 % (803734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.90 % (803734)CaDiCaL version: 2.1.3
% 0.19/1.90 % (803734)Termination reason: Instruction limit
% 0.19/1.90 % (803734)Termination phase: Saturation
% 0.19/1.90 % (803734)Time elapsed: 0.160 s
% 0.19/1.90 % (803734)Peak memory usage: 89 MB
% 0.19/1.90 % (803734)Instructions burned: 181 (million)
% 0.19/1.90 % (803736)Instruction limit reached!
% 0.19/1.90 % (803736)------------------------------
% 0.19/1.90 % (803736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.90 % (803736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.90 % (803736)CaDiCaL version: 2.1.3
% 0.19/1.90 % (803736)Termination reason: Instruction limit
% 0.19/1.90 % (803736)Termination phase: Saturation
% 0.19/1.90 % (803736)Time elapsed: 0.248 s
% 0.19/1.90 % (803736)Peak memory usage: 90 MB
% 0.19/1.90 % (803736)Instructions burned: 259 (million)
% 0.19/1.90 % (803788)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3211498958:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 0.19/1.90 % (803789)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=111066622:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 0.19/1.90 % (803792)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3622711291:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 0.19/1.90 % (803792)Refutation not found, incomplete strategy
% 0.19/1.90 % (803792)------------------------------
% 0.19/1.90 % (803792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.90 % (803792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.90 % (803792)CaDiCaL version: 2.1.3
% 0.19/1.90 % (803792)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.90 % (803792)Time elapsed: 0.002 s
% 0.19/1.90 % (803792)Peak memory usage: 88 MB
% 0.19/1.90 % (803792)Instructions burned: 1 (million)
% 0.19/1.90 % (803792)------------------------------
% 0.19/1.90 % (803792)------------------------------
% 0.19/1.90 % (803730)First to succeed.
% 0.19/1.90 % (803730)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-803617"
% 0.19/1.90 % (803737)Instruction limit reached!
% 0.19/1.90 % (803737)------------------------------
% 0.19/1.90 % (803737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.90 % (803737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.90 % (803737)CaDiCaL version: 2.1.3
% 0.19/1.90 % (803737)Termination reason: Instruction limit
% 0.19/1.90 % (803737)Termination phase: Saturation
% 0.19/1.90 % (803737)Time elapsed: 0.706 s
% 0.19/1.90 % (803737)Peak memory usage: 95 MB
% 0.19/1.90 % (803737)Instructions burned: 1189 (million)
% 0.19/1.90 % (803731)Also succeeded, but the first one will report.
% 0.19/1.90 % (803901)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=3917946098:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 0.19/1.90 % (803730)Refutation found. Thanks to Tanya!
% 0.19/1.90 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.90 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.90 % (803730)------------------------------
% 0.19/1.90 % (803730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.90 % (803730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.90 % (803730)CaDiCaL version: 2.1.3
% 0.19/1.90 % (803730)Termination reason: Refutation
% 0.19/1.90 % (803730)Time elapsed: 0.666 s
% 0.19/1.90 % (803730)Peak memory usage: 129 MB
% 0.19/1.90 % (803730)Instructions burned: 1026 (million)
% 0.19/1.90 % (803730)------------------------------
% 0.19/1.90 % (803730)------------------------------
% 0.19/1.90 % (803617)Success in time 1.047 s
% 0.19/1.90 % Vampire exiting
%------------------------------------------------------------------------------