%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT003-2 : 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 : 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 09:36:33 AM UTC 2026
% Result : Unsatisfiable 5.93s 1.96s
% Output : Refutation 5.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 15 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 64 ( 33 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 2 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 : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(compose(a,b)) != domain(X0)
| compose(compose(a,b),X0) != X1
| codomain(compose(a,b)) != domain(X2)
| compose(compose(a,b),X2) != X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',endomorphism) ).
fof(f12,plain,
! [X2,X0,X1] :
( domain(X0) != codomain(compose(a,b))
| compose(compose(a,b),X0) != X1
| domain(X2) != codomain(compose(a,b))
| compose(compose(a,b),X2) != X1
| X0 = X2 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
codomain(a) = domain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
fof(f14,axiom,
codomain(b) = domain(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_h) ).
fof(f15,axiom,
codomain(b) = domain(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_g) ).
fof(f16,axiom,
compose(b,h) = compose(b,g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bh_equals_bg) ).
fof(f17,negated_conjecture,
g != h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_g_equals_h) ).
fof(f18,plain,
h != g,
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X2,X0] :
( compose(compose(a,b),X0) != compose(compose(a,b),X2)
| domain(X2) != codomain(compose(a,b))
| domain(X0) != codomain(compose(a,b))
| X0 = X2 ),
inference(equality_resolution,[],[f12]) ).
fof(f21,plain,
domain(h) = domain(g),
inference(superposition,[],[f14,f15]) ).
fof(f42,plain,
! [X0] :
( domain(X0) != domain(b)
| codomain(X0) = codomain(compose(a,X0)) ),
inference(superposition,[],[f9,f13]) ).
fof(f59,plain,
! [X0,X1] :
( codomain(X1) != domain(b)
| domain(X0) != domain(h)
| compose(X1,compose(b,X0)) = compose(compose(X1,b),X0) ),
inference(superposition,[],[f10,f14]) ).
fof(f141,plain,
codomain(compose(a,b)) = codomain(b),
inference(equality_resolution,[],[f42]) ).
fof(f142,plain,
codomain(compose(a,b)) = domain(g),
inference(forward_demodulation,[],[f141,f15]) ).
fof(f145,plain,
codomain(compose(a,b)) = domain(h),
inference(forward_demodulation,[],[f142,f21]) ).
fof(f271,plain,
! [X0] :
( domain(b) != domain(b)
| domain(X0) != domain(h)
| compose(compose(a,b),X0) = compose(a,compose(b,X0)) ),
inference(superposition,[],[f59,f13]) ).
fof(f275,plain,
! [X0] :
( domain(X0) != domain(h)
| compose(compose(a,b),X0) = compose(a,compose(b,X0)) ),
inference(trivial_inequality_removal,[],[f271]) ).
fof(f765,plain,
( domain(h) != domain(h)
| compose(compose(a,b),g) = compose(a,compose(b,g)) ),
inference(superposition,[],[f275,f21]) ).
fof(f766,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(equality_resolution,[],[f275]) ).
fof(f767,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(trivial_inequality_removal,[],[f765]) ).
fof(f768,plain,
compose(a,compose(b,h)) = compose(compose(a,b),g),
inference(forward_demodulation,[],[f767,f16]) ).
fof(f771,plain,
! [X0] :
( compose(compose(a,b),X0) != compose(a,compose(b,h))
| domain(X0) != codomain(compose(a,b))
| codomain(compose(a,b)) != domain(h)
| h = X0 ),
inference(superposition,[],[f19,f766]) ).
fof(f772,plain,
! [X0] :
( compose(compose(a,b),X0) != compose(a,compose(b,h))
| domain(X0) != codomain(compose(a,b))
| h = X0 ),
inference(forward_subsumption_resolution,[],[f771,f145]) ).
fof(f775,plain,
! [X0] :
( compose(compose(a,b),X0) != compose(a,compose(b,h))
| domain(X0) != domain(h)
| h = X0 ),
inference(forward_demodulation,[],[f772,f145]) ).
fof(f2569,plain,
( compose(a,compose(b,h)) != compose(a,compose(b,h))
| domain(h) != domain(g)
| h = g ),
inference(superposition,[],[f775,f768]) ).
fof(f2571,plain,
( domain(h) != domain(g)
| h = g ),
inference(trivial_inequality_removal,[],[f2569]) ).
fof(f2572,plain,
h = g,
inference(forward_subsumption_resolution,[],[f2571,f21]) ).
fof(f2573,plain,
$false,
inference(forward_subsumption_resolution,[],[f2572,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.28 % Computer : n014.cluster.edu
% 0.23/0.28 % Model : x86_64 x86_64
% 0.23/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.28 % Memory : 8046.5625MB
% 0.23/0.28 % OS : Linux 6.8.0-71-generic
% 0.23/0.28 % CPULimit : 300
% 0.23/0.28 % WCLimit : 300
% 0.23/0.28 % DateTime : Mon Sep 28 21:12:46 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.33 Running first-order theorem proving
% 0.23/0.33 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
% 5.93/1.96 % (2192202)Input is clausal, will run a generic CNF schedule.
% 5.93/1.96 % (2192217)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2577530645:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.93/1.96 % (2192218)lrs+10_1_sil=8000:sp=occurrence:random_seed=3079826149:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.93/1.96 % (2192215)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=3103319986:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.93/1.96 % (2192220)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=289002417:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.93/1.96 % (2192221)dis-21_1_sil=8000:lcm=predicate:random_seed=2423675690: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)
% 5.93/1.96 % (2192219)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2017275698:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.93/1.96 % (2192221)Refutation not found, incomplete strategy
% 5.93/1.96 % (2192221)------------------------------
% 5.93/1.96 % (2192221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.96 % (2192221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.96 % (2192221)CaDiCaL version: 2.1.3
% 5.93/1.96 % (2192221)Termination reason: Refutation not found, incomplete strategy
% 5.93/1.96 % (2192221)Time elapsed: 0.002 s
% 5.93/1.96 % (2192221)Peak memory usage: 88 MB
% 5.93/1.96 % (2192221)Instructions burned: 1 (million)
% 5.93/1.96 % (2192216)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=542675:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.93/1.96 % (2192218)First to succeed.
% 5.93/1.96 % (2192218)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2192202"
% 5.93/1.96 % (2192219)Instruction limit reached!
% 5.93/1.96 % (2192219)------------------------------
% 5.93/1.96 % (2192219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.96 % (2192219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.96 % (2192219)CaDiCaL version: 2.1.3
% 5.93/1.96 % (2192219)Termination reason: Instruction limit
% 5.93/1.96 % (2192219)Termination phase: Saturation
% 5.93/1.96 % (2192219)Time elapsed: 0.109 s
% 5.93/1.96 % (2192219)Peak memory usage: 88 MB
% 5.93/1.96 % (2192219)Instructions burned: 114 (million)
% 5.93/1.96 % (2192220)Also succeeded, but the first one will report.
% 5.93/1.96 % (2192229)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=2975667328:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 5.93/1.96 % (2192229)Also succeeded, but the first one will report.
% 5.93/1.96 % (2192221)------------------------------
% 5.93/1.96 % (2192221)------------------------------
% 5.93/1.96 % (2192218)Refutation found. Thanks to Tanya!
% 5.93/1.96 % SZS status Unsatisfiable for theBenchmark
% 5.93/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 5.93/1.96 % (2192218)------------------------------
% 5.93/1.96 % (2192218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.96 % (2192218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.96 % (2192218)CaDiCaL version: 2.1.3
% 5.93/1.96 % (2192218)Termination reason: Refutation
% 5.93/1.96 % (2192218)Time elapsed: 0.095 s
% 5.93/1.96 % (2192218)Peak memory usage: 89 MB
% 5.93/1.96 % (2192218)Instructions burned: 102 (million)
% 5.93/1.96 % (2192218)------------------------------
% 5.93/1.96 % (2192218)------------------------------
% 5.93/1.96 % (2192202)Success in time 0.702 s
% 5.93/1.96 % Vampire exiting
%------------------------------------------------------------------------------