%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL009-1 : 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 : n007.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 09:37:37 AM UTC 2026
% Result : Unsatisfiable 8.85s 2.23s
% Output : Refutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 12 unt; 1 def)
% Number of atoms : 22 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 5 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 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(l2,X0),X1) = apply(X1,apply(X0,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_definition) ).
fof(f3,negated_conjecture,
! [X0] : X0 != apply(combinator,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f4,plain,
! [X0] : apply(combinator,X0) != X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f6,plain,
! [X2,X0,X1] : sQ0_eqProxy(apply(apply(apply(b,X0),X1),X2),apply(X0,apply(X1,X2))),
inference(equality_proxy_replacement,[],[f1,f5]) ).
fof(f7,plain,
! [X0,X1] : sQ0_eqProxy(apply(apply(l2,X0),X1),apply(X1,apply(X0,X0))),
inference(equality_proxy_replacement,[],[f2,f5]) ).
fof(f8,plain,
! [X0] : ~ sQ0_eqProxy(apply(combinator,X0),X0),
inference(equality_proxy_replacement,[],[f4,f5]) ).
fof(f9,plain,
! [X2,X3,X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| ~ sQ0_eqProxy(X2,X3)
| sQ0_eqProxy(apply(X0,X2),apply(X1,X3)) ),
inference(equality_proxy_axiom,[],[f5]) ).
fof(f10,plain,
! [X0] : sQ0_eqProxy(X0,X0),
inference(equality_proxy_axiom,[],[f5]) ).
fof(f11,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| sQ0_eqProxy(X1,X0) ),
inference(equality_proxy_axiom,[],[f5]) ).
fof(f12,plain,
! [X2,X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| ~ sQ0_eqProxy(X1,X2)
| sQ0_eqProxy(X0,X2) ),
inference(equality_proxy_axiom,[],[f5]) ).
fof(f13,plain,
! [X0] : ~ sQ0_eqProxy(X0,apply(combinator,X0)),
inference(forward_literal_rewriting,[],[f8,f11]) ).
fof(f19,plain,
! [X0,X1] : ~ sQ0_eqProxy(apply(X0,X1),apply(apply(apply(b,combinator),X0),X1)),
inference(unit_resulting_resolution,[],[f12,f6,f13]) ).
fof(f33,plain,
! [X0,X1] : ~ sQ0_eqProxy(apply(X0,apply(X1,X1)),apply(apply(apply(b,combinator),apply(l2,X1)),X0)),
inference(unit_resulting_resolution,[],[f12,f7,f19]) ).
fof(f93,plain,
$false,
inference(unit_resulting_resolution,[],[f9,f6,f10,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n007.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Mon Sep 28 21:27:25 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.29 Running first-order theorem proving
% 0.10/0.29 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
% 8.85/2.23 % (2867317)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.85/2.23 % (2867329)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4093880458:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 8.85/2.23 % (2867330)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2454186385:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 8.85/2.23 % (2867331)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2938247032:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 8.85/2.23 % (2867326)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=123638505:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 8.85/2.23 % (2867327)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2802948482:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 8.85/2.23 % (2867328)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=506865721:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 8.85/2.23 % (2867325)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=814763886:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 8.85/2.23 % (2867329)Instruction limit reached!
% 8.85/2.23 % (2867329)------------------------------
% 8.85/2.23 % (2867329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.85/2.23 % (2867329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/2.23 % (2867329)CaDiCaL version: 2.1.3
% 8.85/2.23 % (2867329)Termination reason: Instruction limit
% 8.85/2.23 % (2867329)Termination phase: Saturation
% 8.85/2.23 % (2867329)Time elapsed: 0.089 s
% 8.85/2.23 % (2867329)Peak memory usage: 88 MB
% 8.85/2.23 % (2867329)Instructions burned: 182 (million)
% 8.85/2.23 % (2867328)Instruction limit reached!
% 8.85/2.23 % (2867328)------------------------------
% 8.85/2.23 % (2867328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.85/2.23 % (2867328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/2.23 % (2867328)CaDiCaL version: 2.1.3
% 8.85/2.23 % (2867328)Termination reason: Instruction limit
% 8.85/2.23 % (2867328)Termination phase: Saturation
% 8.85/2.23 % (2867328)Time elapsed: 0.132 s
% 8.85/2.23 % (2867328)Peak memory usage: 88 MB
% 8.85/2.23 % (2867328)Instructions burned: 136 (million)
% 8.85/2.23 % (2867330)Instruction limit reached!
% 8.85/2.23 % (2867330)------------------------------
% 8.85/2.23 % (2867330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.85/2.23 % (2867330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/2.23 % (2867330)CaDiCaL version: 2.1.3
% 8.85/2.23 % (2867330)Termination reason: Instruction limit
% 8.85/2.23 % (2867330)Termination phase: Saturation
% 8.85/2.23 % (2867330)Time elapsed: 0.260 s
% 8.85/2.23 % (2867330)Peak memory usage: 90 MB
% 8.85/2.23 % (2867330)Instructions burned: 258 (million)
% 8.85/2.23 % (2867339)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4070728745:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 8.85/2.23 % (2867340)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3860766277:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 8.85/2.23 % (2867341)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3434401935:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 8.85/2.23 % (2867341)First to succeed.
% 8.85/2.23 % (2867341)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2867317"
% 8.85/2.23 % (2867341)Refutation found. Thanks to Tanya!
% 8.85/2.23 % SZS status Unsatisfiable for theBenchmark
% 8.85/2.23 % SZS output start Proof for theBenchmark
% See solution above
% 8.85/2.23 % (2867341)------------------------------
% 8.85/2.23 % (2867341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.85/2.23 % (2867341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/2.23 % (2867341)CaDiCaL version: 2.1.3
% 8.85/2.23 % (2867341)Termination reason: Refutation
% 8.85/2.23 % (2867341)Time elapsed: 0.006 s
% 8.85/2.23 % (2867341)Peak memory usage: 88 MB
% 8.85/2.23 % (2867341)Instructions burned: 4 (million)
% 8.85/2.23 % (2867341)------------------------------
% 8.85/2.23 % (2867341)------------------------------
% 8.85/2.23 % (2867317)Success in time 1.127 s
% 8.85/2.23 % Vampire exiting
%------------------------------------------------------------------------------