%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT018-3 : 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 : n019.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 09:36:39 AM UTC 2026
% Result : Unsatisfiable 3.89s 1.22s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 15 unt; 3 def)
% Number of atoms : 104 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 106 ( 55 ~; 48 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ~ there_exists(domain(X0))
| there_exists(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f5,axiom,
! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f6,axiom,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f7,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f8,axiom,
! [X0,X1] :
( domain(X0) != codomain(X1)
| ~ there_exists(domain(X0))
| there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
fof(f20,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f21,axiom,
there_exists(compose(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f22,negated_conjecture,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_bc_exists) ).
fof(f28,plain,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(X0) ),
inference(resolution,[],[f6,f4]) ).
fof(f33,plain,
there_exists(b),
inference(resolution,[],[f28,f21]) ).
fof(f39,plain,
domain(b) = codomain(c),
inference(resolution,[],[f7,f21]) ).
fof(f40,plain,
! [X0] :
( domain(X0) = codomain(domain(X0))
| ~ there_exists(X0) ),
inference(superposition,[],[f7,f10]) ).
fof(f41,plain,
! [X0] :
( codomain(X0) = domain(codomain(X0))
| ~ there_exists(X0) ),
inference(superposition,[],[f7,f11]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) ),
inference(superposition,[],[f7,f9]) ).
fof(f63,definition,
( spl0_1
<=> ! [X0] : ~ there_exists(compose(b,X0)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f64,plain,
( ! [X0] : ~ there_exists(compose(b,X0))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f72,plain,
! [X0] :
( domain(X0) != domain(b)
| ~ there_exists(domain(X0))
| there_exists(compose(X0,c)) ),
inference(superposition,[],[f8,f39]) ).
fof(f75,plain,
( ~ there_exists(domain(b))
| there_exists(c) ),
inference(superposition,[],[f5,f39]) ).
fof(f77,definition,
( spl0_3
<=> there_exists(c) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f79,plain,
( there_exists(c)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl0_4
<=> there_exists(domain(b)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f82,plain,
( there_exists(domain(b))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( ~ there_exists(domain(b))
| spl0_4 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f75,f81,f77]) ).
fof(f114,plain,
( domain(b) = domain(domain(b))
| ~ there_exists(c) ),
inference(superposition,[],[f41,f39]) ).
fof(f124,plain,
( domain(b) = domain(domain(b))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f114,f79]) ).
fof(f153,plain,
( domain(b) = codomain(domain(b))
| ~ there_exists(domain(b))
| ~ spl0_3 ),
inference(superposition,[],[f40,f124]) ).
fof(f159,plain,
( domain(b) = codomain(domain(b))
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f153,f82]) ).
fof(f273,plain,
! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) ),
inference(superposition,[],[f48,f10]) ).
fof(f816,plain,
codomain(domain(b)) = domain(compose(a,b)),
inference(resolution,[],[f273,f20]) ).
fof(f837,plain,
( domain(b) = domain(compose(a,b))
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f816,f159]) ).
fof(f2336,plain,
( domain(b) != domain(b)
| ~ there_exists(domain(b))
| there_exists(compose(compose(a,b),c))
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f72,f837]) ).
fof(f2345,plain,
( ~ there_exists(domain(b))
| there_exists(compose(compose(a,b),c))
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f2336]) ).
fof(f2352,plain,
( there_exists(compose(compose(a,b),c))
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f2345,f82]) ).
fof(f2359,plain,
( there_exists(compose(a,compose(b,c)))
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f2352,f9]) ).
fof(f2362,plain,
( $false
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f2359,f22]) ).
fof(f2363,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f2362]) ).
fof(f2552,plain,
( ! [X0] : ~ there_exists(compose(b,X0))
| spl0_4 ),
inference(resolution,[],[f83,f6]) ).
fof(f2589,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f2552,f81,f63]) ).
fof(f2644,plain,
( ~ there_exists(b)
| ~ spl0_1 ),
inference(superposition,[],[f64,f10]) ).
fof(f2655,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f2644,f33]) ).
fof(f2656,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f2655]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f84]) ).
cnf(s14,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f2363]) ).
cnf(s39,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f2589]) ).
cnf(s45,plain,
~ spl0_1,
inference(sat_conversion,[],[f2656]) ).
cnf(s48,plain,
spl0_4,
inference(rat,[],[s39,s45]) ).
cnf(s54,plain,
~ spl0_3,
inference(rat,[],[s14,s48]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s2,s48,s54]) ).
fof(f2676,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.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 21:13:49 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.89/1.22 % (289754)Input is clausal, will run a generic CNF schedule.
% 3.89/1.22 % (289765)dis-21_1_sil=8000:lcm=predicate:random_seed=1334659832: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)
% 3.89/1.22 % (289765)Instruction limit reached!
% 3.89/1.22 % (289765)------------------------------
% 3.89/1.22 % (289765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.22 % (289765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.22 % (289765)CaDiCaL version: 2.1.3
% 3.89/1.22 % (289765)Termination reason: Instruction limit
% 3.89/1.22 % (289765)Termination phase: Saturation
% 3.89/1.22 % (289765)Time elapsed: 0.032 s
% 3.89/1.22 % (289765)Peak memory usage: 90 MB
% 3.89/1.22 % (289765)Instructions burned: 121 (million)
% 3.89/1.22 % (289764)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1505670638:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.89/1.22 % (289762)lrs+10_1_sil=8000:sp=occurrence:random_seed=172353300:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.89/1.22 % (289760)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2858086623:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.89/1.22 % (289763)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1131224373:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.89/1.22 % (289759)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=1370725173:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.89/1.22 % (289761)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2602115936:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.89/1.22 % (289762)Refutation not found, incomplete strategy
% 3.89/1.22 % (289762)------------------------------
% 3.89/1.22 % (289762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.22 % (289762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.22 % (289762)CaDiCaL version: 2.1.3
% 3.89/1.22 % (289762)Termination reason: Refutation not found, incomplete strategy
% 3.89/1.22 % (289762)Time elapsed: 0.001 s
% 3.89/1.22 % (289762)Peak memory usage: 88 MB
% 3.89/1.22 % (289764)First to succeed.
% 3.89/1.22 % (289764)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-289754"
% 3.89/1.22 % (289763)Instruction limit reached!
% 3.89/1.22 % (289763)------------------------------
% 3.89/1.22 % (289763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.22 % (289763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.22 % (289763)CaDiCaL version: 2.1.3
% 3.89/1.22 % (289763)Termination reason: Instruction limit
% 3.89/1.22 % (289763)Termination phase: Saturation
% 3.89/1.22 % (289763)Time elapsed: 0.066 s
% 3.89/1.22 % (289763)Peak memory usage: 88 MB
% 3.89/1.22 % (289763)Instructions burned: 115 (million)
% 3.89/1.22 % (289767)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1090674294:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.89/1.22 % (289767)Refutation not found, incomplete strategy
% 3.89/1.22 % (289767)------------------------------
% 3.89/1.22 % (289767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.22 % (289767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.22 % (289767)CaDiCaL version: 2.1.3
% 3.89/1.22 % (289767)Termination reason: Refutation not found, incomplete strategy
% 3.89/1.22 % (289767)Time elapsed: 0.001 s
% 3.89/1.22 % (289767)Peak memory usage: 88 MB
% 3.89/1.22 % (289767)Instructions burned: 1 (million)
% 3.89/1.22 % (289774)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2237575086:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.89/1.22 % (289767)------------------------------
% 3.89/1.22 % (289767)------------------------------
% 3.89/1.22 % (289762)------------------------------
% 3.89/1.22 % (289762)------------------------------
% 3.89/1.22 % (289777)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1759025879:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 3.89/1.22 % (289774)Instruction limit reached!
% 3.89/1.22 % (289774)------------------------------
% 3.89/1.22 % (289774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.22 % (289774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.22 % (289774)CaDiCaL version: 2.1.3
% 3.89/1.22 % (289774)Termination reason: Instruction limit
% 3.89/1.22 % (289774)Termination phase: Saturation
% 3.89/1.22 % (289774)Time elapsed: 0.119 s
% 3.89/1.22 % (289774)Peak memory usage: 89 MB
% 3.89/1.22 % (289774)Instructions burned: 189 (million)
% 3.89/1.22 % (289764)Refutation found. Thanks to Tanya!
% 3.89/1.22 % SZS status Unsatisfiable for theBenchmark
% 3.89/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.22 % (289764)------------------------------
% 3.89/1.22 % (289764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.22 % (289764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.22 % (289764)CaDiCaL version: 2.1.3
% 3.89/1.22 % (289764)Termination reason: Refutation
% 3.89/1.22 % (289764)Time elapsed: 0.062 s
% 3.89/1.22 % (289764)Peak memory usage: 90 MB
% 3.89/1.22 % (289764)Instructions burned: 102 (million)
% 3.89/1.22 % (289764)------------------------------
% 3.89/1.22 % (289764)------------------------------
% 3.89/1.22 % (289754)Success in time 0.47 s
% 3.89/1.22 % Vampire exiting
%------------------------------------------------------------------------------