%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:39:45 PM UTC 2026
% Result : Unsatisfiable 2.87s 1.25s
% Output : Refutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 25 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 30 ( 17 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f166,axiom,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_sets_equal) ).
fof(f186,axiom,
! [X2,X0,X1] :
( subset(apply(X2,apply(X0,X1)),apply(compose(X2,X0),X1))
| ~ member(X1,domain_of(X0))
| ~ function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_composition1) ).
fof(f187,axiom,
! [X2,X0,X1] :
( subset(apply(compose(X1,X0),X2),apply(X1,apply(X0,X2)))
| ~ function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_composition2) ).
fof(f188,axiom,
function(a_function),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_function) ).
fof(f189,axiom,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_domain) ).
fof(f190,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_apply_for_composition3) ).
fof(f271,plain,
! [X2,X0,X1] :
( ~ member(X0,domain_of(X1))
| ~ function(X1)
| ~ subset(apply(compose(X2,X1),X0),apply(X2,apply(X1,X0)))
| apply(compose(X2,X1),X0) = apply(X2,apply(X1,X0)) ),
inference(resolution,[],[f186,f166]) ).
fof(f273,plain,
! [X2,X0,X1] :
( apply(compose(X2,X1),X0) = apply(X2,apply(X1,X0))
| ~ function(X1)
| ~ member(X0,domain_of(X1)) ),
inference(forward_subsumption_resolution,[],[f271,f187]) ).
fof(f330,plain,
( apply(another_function,apply(a_function,a)) != apply(another_function,apply(a_function,a))
| ~ function(a_function)
| ~ member(a,domain_of(a_function)) ),
inference(superposition,[],[f190,f273]) ).
fof(f347,plain,
( ~ function(a_function)
| ~ member(a,domain_of(a_function)) ),
inference(trivial_inequality_removal,[],[f330]) ).
fof(f351,plain,
~ member(a,domain_of(a_function)),
inference(forward_subsumption_resolution,[],[f347,f188]) ).
fof(f353,plain,
$false,
inference(forward_subsumption_resolution,[],[f351,f189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n003.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 00:21:57 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.87/1.25 % (1071131)Input is clausal, will run a generic CNF schedule.
% 2.87/1.25 % (1071175)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=512864886:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.87/1.25 % (1071174)lrs+10_1_sil=8000:sp=occurrence:random_seed=3592974326:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.87/1.25 % (1071176)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4241685037:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.87/1.25 % (1071172)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1301578469:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.87/1.25 % (1071177)dis-21_1_sil=8000:lcm=predicate:random_seed=520301663:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.87/1.25 % (1071171)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2173047083:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.87/1.25 % (1071173)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3276313483:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.87/1.25 % (1071175)First to succeed.
% 2.87/1.25 % (1071175)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1071131"
% 2.87/1.25 % (1071174)Also succeeded, but the first one will report.
% 2.87/1.25 % (1071177)Instruction limit reached!
% 2.87/1.25 % (1071177)------------------------------
% 2.87/1.25 % (1071177)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.25 % (1071177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.25 % (1071177)CaDiCaL version: 2.1.3
% 2.87/1.25 % (1071177)Termination reason: Instruction limit
% 2.87/1.25 % (1071177)Termination phase: Saturation
% 2.87/1.25 % (1071177)Time elapsed: 0.069 s
% 2.87/1.25 % (1071177)Peak memory usage: 89 MB
% 2.87/1.25 % (1071177)Instructions burned: 119 (million)
% 2.87/1.25 % (1071176)Instruction limit reached!
% 2.87/1.25 % (1071176)------------------------------
% 2.87/1.25 % (1071176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.25 % (1071176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.25 % (1071176)CaDiCaL version: 2.1.3
% 2.87/1.25 % (1071176)Termination reason: Instruction limit
% 2.87/1.25 % (1071176)Termination phase: Saturation
% 2.87/1.25 % (1071176)Time elapsed: 0.145 s
% 2.87/1.25 % (1071176)Peak memory usage: 90 MB
% 2.87/1.25 % (1071176)Instructions burned: 180 (million)
% 2.87/1.25 % (1071175)Refutation found. Thanks to Tanya!
% 2.87/1.25 % SZS status Unsatisfiable for theBenchmark
% 2.87/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.87/1.25 % (1071175)------------------------------
% 2.87/1.25 % (1071175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.25 % (1071175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.25 % (1071175)CaDiCaL version: 2.1.3
% 2.87/1.25 % (1071175)Termination reason: Refutation
% 2.87/1.25 % (1071175)Time elapsed: 0.006 s
% 2.87/1.25 % (1071175)Peak memory usage: 88 MB
% 2.87/1.25 % (1071175)Instructions burned: 12 (million)
% 2.87/1.25 % (1071175)------------------------------
% 2.87/1.25 % (1071175)------------------------------
% 2.87/1.25 % (1071131)Success in time 0.344 s
% 2.87/1.25 % Vampire exiting
%------------------------------------------------------------------------------