%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT004-2 : 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 : n009.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 09:36:34 AM UTC 2026
% Result : Unsatisfiable 4.92s 1.47s
% Output : Refutation 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 19 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 57 ( 30 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( codomain(X0) != domain(X1)
| domain(compose(X0,X1)) = domain(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_domain1) ).
fof(f8,plain,
! [X0,X1] :
( codomain(X0) != domain(X1)
| domain(X0) = domain(compose(X0,X1)) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( codomain(X0) != domain(X1)
| codomain(compose(X0,X1)) = codomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_domain2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( codomain(X1) != domain(X2)
| codomain(X0) != domain(X1)
| compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_property) ).
fof(f11,axiom,
! [X2,X0,X1] :
( codomain(a) != domain(X0)
| compose(a,X0) != X1
| codomain(a) != domain(X2)
| compose(a,X2) != X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epimorphism1) ).
fof(f12,plain,
! [X2,X0,X1] :
( domain(X0) != codomain(a)
| compose(a,X0) != X1
| domain(X2) != codomain(a)
| compose(a,X2) != X1
| X0 = X2 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X2,X0,X1] :
( codomain(b) != domain(X0)
| compose(b,X0) != X1
| codomain(b) != domain(X2)
| compose(b,X2) != X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epimorphism2) ).
fof(f14,plain,
! [X2,X0,X1] :
( domain(X0) != codomain(b)
| compose(b,X0) != X1
| domain(X2) != codomain(b)
| compose(b,X2) != X1
| X0 = X2 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
codomain(a) = domain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
fof(f16,axiom,
codomain(compose(a,b)) = domain(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_h) ).
fof(f17,axiom,
codomain(compose(a,b)) = domain(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_g) ).
fof(f18,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
fof(f19,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
fof(f20,plain,
! [X2,X0] :
( compose(a,X0) != compose(a,X2)
| domain(X2) != codomain(a)
| domain(X0) != codomain(a)
| X0 = X2 ),
inference(equality_resolution,[],[f12]) ).
fof(f21,plain,
! [X2,X0] :
( compose(b,X0) != compose(b,X2)
| domain(X2) != codomain(b)
| domain(X0) != codomain(b)
| X0 = X2 ),
inference(equality_resolution,[],[f14]) ).
fof(f23,plain,
codomain(b) = codomain(compose(a,b)),
inference(unit_resulting_resolution,[],[f9,f15]) ).
fof(f31,plain,
codomain(b) = domain(h),
inference(backward_demodulation,[],[f16,f23]) ).
fof(f32,plain,
codomain(b) = domain(g),
inference(backward_demodulation,[],[f17,f23]) ).
fof(f35,plain,
domain(b) = domain(compose(b,h)),
inference(unit_resulting_resolution,[],[f8,f31]) ).
fof(f38,plain,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(unit_resulting_resolution,[],[f10,f15,f31]) ).
fof(f45,plain,
codomain(a) = domain(compose(b,h)),
inference(forward_demodulation,[],[f35,f15]) ).
fof(f47,plain,
compose(compose(a,b),g) = compose(a,compose(b,h)),
inference(backward_demodulation,[],[f18,f38]) ).
fof(f50,plain,
domain(b) = domain(compose(b,g)),
inference(unit_resulting_resolution,[],[f8,f32]) ).
fof(f53,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(unit_resulting_resolution,[],[f10,f15,f32]) ).
fof(f60,plain,
codomain(a) = domain(compose(b,g)),
inference(forward_demodulation,[],[f50,f15]) ).
fof(f62,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(forward_demodulation,[],[f53,f47]) ).
fof(f85,plain,
compose(b,h) != compose(b,g),
inference(unit_resulting_resolution,[],[f21,f19,f32,f31]) ).
fof(f138,plain,
compose(a,compose(b,h)) != compose(a,compose(b,g)),
inference(unit_resulting_resolution,[],[f20,f85,f45,f60]) ).
fof(f150,plain,
$false,
inference(forward_subsumption_resolution,[],[f138,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.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 21:13:00 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.92/1.47 % (3483401)Input is clausal, will run a generic CNF schedule.
% 4.92/1.47 % (3483539)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=65804839:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.92/1.47 % (3483538)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1296595743:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.92/1.47 % (3483536)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=1805868482:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.92/1.47 % (3483541)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1716483154:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.92/1.47 % (3483540)lrs+10_1_sil=8000:sp=occurrence:random_seed=2674750415:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.92/1.47 % (3483543)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=838406133:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.92/1.47 % (3483544)dis-21_1_sil=8000:lcm=predicate:random_seed=1752031425: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)
% 4.92/1.47 % (3483544)Refutation not found, incomplete strategy
% 4.92/1.47 % (3483544)------------------------------
% 4.92/1.47 % (3483544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.47 % (3483544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.47 % (3483544)CaDiCaL version: 2.1.3
% 4.92/1.47 % (3483544)Termination reason: Refutation not found, incomplete strategy
% 4.92/1.47 % (3483544)Time elapsed: 0.002 s
% 4.92/1.47 % (3483544)Peak memory usage: 88 MB
% 4.92/1.47 % (3483544)Instructions burned: 1 (million)
% 4.92/1.47 % (3483541)Instruction limit reached!
% 4.92/1.47 % (3483541)------------------------------
% 4.92/1.47 % (3483541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.47 % (3483541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.47 % (3483541)CaDiCaL version: 2.1.3
% 4.92/1.47 % (3483541)Termination reason: Instruction limit
% 4.92/1.47 % (3483541)Termination phase: Saturation
% 4.92/1.47 % (3483541)Time elapsed: 0.059 s
% 4.92/1.47 % (3483541)Peak memory usage: 88 MB
% 4.92/1.47 % (3483541)Instructions burned: 115 (million)
% 4.92/1.47 % (3483540)Instruction limit reached!
% 4.92/1.47 % (3483540)------------------------------
% 4.92/1.47 % (3483540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.47 % (3483540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.47 % (3483540)CaDiCaL version: 2.1.3
% 4.92/1.47 % (3483540)Termination reason: Instruction limit
% 4.92/1.47 % (3483540)Termination phase: Saturation
% 4.92/1.47 % (3483540)Time elapsed: 0.059 s
% 4.92/1.47 % (3483540)Peak memory usage: 89 MB
% 4.92/1.47 % (3483540)Instructions burned: 107 (million)
% 4.92/1.47 % (3483543)Instruction limit reached!
% 4.92/1.47 % (3483543)------------------------------
% 4.92/1.47 % (3483543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.47 % (3483543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.47 % (3483543)CaDiCaL version: 2.1.3
% 4.92/1.47 % (3483543)Termination reason: Instruction limit
% 4.92/1.47 % (3483543)Termination phase: Saturation
% 4.92/1.47 % (3483543)Time elapsed: 0.103 s
% 4.92/1.47 % (3483543)Peak memory usage: 89 MB
% 4.92/1.47 % (3483543)Instructions burned: 181 (million)
% 4.92/1.47 % (3483557)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=1687137237:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.92/1.47 % (3483558)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1892933001:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 4.92/1.47 % (3483558)First to succeed.
% 4.92/1.47 % (3483558)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3483401"
% 4.92/1.47 % (3483559)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=381466168:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.92/1.47 % (3483559)Also succeeded, but the first one will report.
% 4.92/1.47 % (3483544)------------------------------
% 4.92/1.47 % (3483544)------------------------------
% 4.92/1.47 % (3483557)Also succeeded, but the first one will report.
% 4.92/1.47 % (3483539)Also succeeded, but the first one will report.
% 4.92/1.47 % (3483563)lrs+10_64_to=lpo:sil=8000:random_seed=1109226723:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 4.92/1.47 % (3483563)Also succeeded, but the first one will report.
% 4.92/1.47 % (3483558)Refutation found. Thanks to Tanya!
% 4.92/1.47 % SZS status Unsatisfiable for theBenchmark
% 4.92/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 4.92/1.47 % (3483558)------------------------------
% 4.92/1.47 % (3483558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.47 % (3483558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.47 % (3483558)CaDiCaL version: 2.1.3
% 4.92/1.47 % (3483558)Termination reason: Refutation
% 4.92/1.47 % (3483558)Time elapsed: 0.008 s
% 4.92/1.47 % (3483558)Peak memory usage: 88 MB
% 4.92/1.47 % (3483558)Instructions burned: 11 (million)
% 4.92/1.47 % (3483558)------------------------------
% 4.92/1.47 % (3483558)------------------------------
% 4.92/1.47 % (3483401)Success in time 0.606 s
% 4.92/1.47 % Vampire exiting
%------------------------------------------------------------------------------