%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL044-6 : 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 : n014.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 09:37:44 AM UTC 2026
% Result : Unsatisfiable 8.73s 2.01s
% Output : Refutation 8.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 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 : 12 ( 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 : 33 ( 33 !; 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(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),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(n,apply(apply(b,X0),X1)),X3),X2) = apply(apply(apply(X0,apply(X1,X2)),X3),X2),
inference(superposition,[],[f2,f1]) ).
fof(f9,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(b,X0)),X2),X1) = apply(apply(X0,apply(X1,X2)),X1),
inference(superposition,[],[f2,f1]) ).
fof(f11,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(X0,X2)),X2),X1) = apply(apply(apply(apply(n,X0),X1),X2),X1),
inference(superposition,[],[f2,f2]) ).
fof(f15,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(X0,X2)),X2),X1) = apply(apply(apply(n,apply(n,X0)),X2),X1),
inference(forward_demodulation,[],[f11,f2]) ).
fof(f19,plain,
! [X0] : apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f23,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,X0))),
inference(forward_demodulation,[],[f19,f1]) ).
fof(f47,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X2,X1),X2)),
inference(superposition,[],[f1,f9]) ).
fof(f153,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(superposition,[],[f1,f6]) ).
fof(f218,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),
inference(superposition,[],[f23,f153]) ).
fof(f250,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f218,f15]) ).
fof(f311,plain,
! [X0,X1] : apply(apply(X0,X1),apply(X0,X1)) = apply(apply(apply(n,apply(n,apply(b,b))),X0),X1),
inference(superposition,[],[f153,f15]) ).
fof(f409,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),apply(n,apply(b,apply(b,X0)))),
inference(superposition,[],[f250,f311]) ).
fof(f452,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(superposition,[],[f47,f409]) ).
fof(f516,plain,
apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
inference(superposition,[],[f4,f452]) ).
fof(f517,plain,
$false,
inference(trivial_inequality_removal,[],[f516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % 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 21:30:45 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 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
% 8.73/2.01 % (2207923)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.73/2.01 % (2207931)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2405287485:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.73/2.01 % (2207930)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=502337599:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.73/2.01 % (2207934)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=496062633:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.73/2.01 % (2207933)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1145859149:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.73/2.01 % (2207928)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=4106737401:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.73/2.01 % (2207932)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2831775907:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.73/2.01 % (2207929)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=3013825234:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.73/2.01 % (2207931)Instruction limit reached!
% 8.73/2.01 % (2207931)------------------------------
% 8.73/2.01 % (2207931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.73/2.01 % (2207931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.73/2.01 % (2207931)CaDiCaL version: 2.1.3
% 8.73/2.01 % (2207931)Termination reason: Instruction limit
% 8.73/2.01 % (2207931)Termination phase: Saturation
% 8.73/2.01 % (2207931)Time elapsed: 0.046 s
% 8.73/2.01 % (2207931)Peak memory usage: 89 MB
% 8.73/2.01 % (2207931)Instructions burned: 139 (million)
% 8.73/2.01 % (2207932)Instruction limit reached!
% 8.73/2.01 % (2207932)------------------------------
% 8.73/2.01 % (2207932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.73/2.01 % (2207932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.73/2.01 % (2207932)CaDiCaL version: 2.1.3
% 8.73/2.01 % (2207932)Termination reason: Instruction limit
% 8.73/2.01 % (2207932)Termination phase: Saturation
% 8.73/2.01 % (2207932)Time elapsed: 0.102 s
% 8.73/2.01 % (2207932)Peak memory usage: 89 MB
% 8.73/2.01 % (2207932)Instructions burned: 181 (million)
% 8.73/2.01 % (2207942)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3162630210:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 8.73/2.01 % (2207933)Instruction limit reached!
% 8.73/2.01 % (2207933)------------------------------
% 8.73/2.01 % (2207933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.73/2.01 % (2207933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.73/2.01 % (2207933)CaDiCaL version: 2.1.3
% 8.73/2.01 % (2207933)Termination reason: Instruction limit
% 8.73/2.01 % (2207933)Termination phase: Saturation
% 8.73/2.01 % (2207933)Time elapsed: 0.165 s
% 8.73/2.01 % (2207933)Peak memory usage: 91 MB
% 8.73/2.01 % (2207933)Instructions burned: 261 (million)
% 8.73/2.01 % (2207943)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1483941837:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 8.73/2.01 % (2207945)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1680359922:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 8.73/2.01 % (2207945)Refutation not found, incomplete strategy
% 8.73/2.01 % (2207945)------------------------------
% 8.73/2.01 % (2207945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.73/2.01 % (2207945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.73/2.01 % (2207945)CaDiCaL version: 2.1.3
% 8.73/2.01 % (2207945)Termination reason: Refutation not found, incomplete strategy
% 8.73/2.01 % (2207945)Time elapsed: 0.002 s
% 8.73/2.01 % (2207945)Peak memory usage: 88 MB
% 8.73/2.01 % (2207945)Instructions burned: 1 (million)
% 8.73/2.01 % (2207945)------------------------------
% 8.73/2.01 % (2207945)------------------------------
% 8.73/2.01 % (2207934)Instruction limit reached!
% 8.73/2.01 % (2207934)------------------------------
% 8.73/2.01 % (2207934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.73/2.01 % (2207934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.73/2.01 % (2207934)CaDiCaL version: 2.1.3
% 8.73/2.01 % (2207934)Termination reason: Instruction limit
% 8.73/2.01 % (2207934)Termination phase: Saturation
% 8.73/2.01 % (2207934)Time elapsed: 0.642 s
% 8.73/2.01 % (2207934)Peak memory usage: 98 MB
% 8.73/2.01 % (2207934)Instructions burned: 1188 (million)
% 8.73/2.01 % (2207948)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=4091818463: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)
% 8.73/2.01 % (2207929)First to succeed.
% 8.73/2.01 % (2207929)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2207923"
% 8.73/2.01 % (2207949)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=2084206116:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 8.73/2.01 % (2207942)Instruction limit reached!
% 8.73/2.01 % (2207942)------------------------------
% 8.73/2.01 % (2207942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.73/2.01 % (2207942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.73/2.01 % (2207942)CaDiCaL version: 2.1.3
% 8.73/2.01 % (2207942)Termination reason: Instruction limit
% 8.73/2.01 % (2207942)Termination phase: Saturation
% 8.73/2.01 % (2207942)Time elapsed: 0.713 s
% 8.73/2.01 % (2207942)Peak memory usage: 138 MB
% 8.73/2.01 % (2207942)Instructions burned: 2051 (million)
% 8.73/2.01 % (2207948)Instruction limit reached!
% 8.73/2.01 % (2207948)------------------------------
% 8.73/2.01 % (2207948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.73/2.01 % (2207948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.73/2.01 % (2207948)CaDiCaL version: 2.1.3
% 8.73/2.01 % (2207948)Termination reason: Instruction limit
% 8.73/2.01 % (2207948)Termination phase: Saturation
% 8.73/2.01 % (2207948)Time elapsed: 0.171 s
% 8.73/2.01 % (2207948)Peak memory usage: 90 MB
% 8.73/2.01 % (2207948)Instructions burned: 317 (million)
% 8.73/2.01 % (2207929)Refutation found. Thanks to Tanya!
% 8.73/2.01 % SZS status Unsatisfiable for theBenchmark
% 8.73/2.01 % SZS output start Proof for theBenchmark
% See solution above
% 8.73/2.01 % (2207929)------------------------------
% 8.73/2.01 % (2207929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.73/2.01 % (2207929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.73/2.01 % (2207929)CaDiCaL version: 2.1.3
% 8.73/2.01 % (2207929)Termination reason: Refutation
% 8.73/2.01 % (2207929)Time elapsed: 0.728 s
% 8.73/2.01 % (2207929)Peak memory usage: 130 MB
% 8.73/2.01 % (2207929)Instructions burned: 1144 (million)
% 8.73/2.01 % (2207929)------------------------------
% 8.73/2.01 % (2207929)------------------------------
% 8.73/2.01 % (2207923)Success in time 1.157 s
% 8.73/2.01 % Vampire exiting
%------------------------------------------------------------------------------