%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT004-3 : 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 : n018.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 3.50s 1.23s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f21,axiom,
! [X2,X0,X1] :
( compose(X0,a) != X1
| compose(X2,a) != X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( compose(X0,b) != X1
| compose(X2,b) != X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product2) ).
fof(f24,axiom,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_ab_equals_g_ab) ).
fof(f25,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
fof(f26,plain,
! [X2,X0] :
( compose(X0,a) != compose(X2,a)
| X0 = X2 ),
inference(equality_resolution,[],[f21]) ).
fof(f27,plain,
! [X2,X0] :
( compose(X0,b) != compose(X2,b)
| X0 = X2 ),
inference(equality_resolution,[],[f22]) ).
fof(f35,plain,
! [X2,X0,X1] :
( compose(X2,b) != compose(X0,compose(X1,b))
| compose(X0,X1) = X2 ),
inference(superposition,[],[f27,f9]) ).
fof(f46,plain,
! [X0] :
( compose(X0,b) != compose(h,compose(a,b))
| compose(g,a) = X0 ),
inference(superposition,[],[f35,f24]) ).
fof(f53,plain,
! [X0,X1] :
( compose(h,compose(a,b)) != compose(X0,compose(X1,b))
| compose(X0,X1) = compose(g,a) ),
inference(superposition,[],[f46,f9]) ).
fof(f89,plain,
compose(g,a) = compose(h,a),
inference(equality_resolution,[],[f53]) ).
fof(f94,plain,
! [X0] :
( compose(X0,a) != compose(h,a)
| g = X0 ),
inference(superposition,[],[f26,f89]) ).
fof(f107,plain,
h = g,
inference(equality_resolution,[],[f94]) ).
fof(f108,plain,
$false,
inference(forward_subsumption_resolution,[],[f107,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.25 % Computer : n018.cluster.edu
% 0.12/0.25 % Model : x86_64 x86_64
% 0.12/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.25 % Memory : 8046.5625MB
% 0.12/0.25 % OS : Linux 6.8.0-71-generic
% 0.12/0.25 % CPULimit : 300
% 0.12/0.25 % WCLimit : 300
% 0.12/0.25 % DateTime : Mon Sep 28 21:15:11 UTC 2026
% 0.12/0.25 % CPUTime :
% 0.12/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 Running first-order theorem proving
% 0.12/0.29 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
% 3.50/1.23 % (3794479)Input is clausal, will run a generic CNF schedule.
% 3.50/1.23 % (3794527)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=420823589:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.50/1.23 % (3794525)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1506051822:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.50/1.23 % (3794530)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2565799848:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.50/1.23 % (3794524)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=1050980888:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.50/1.23 % (3794532)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4185644483:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.50/1.23 % (3794529)lrs+10_1_sil=8000:sp=occurrence:random_seed=2233426662:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.50/1.23 % (3794534)dis-21_1_sil=8000:lcm=predicate:random_seed=3601860807: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)
% 3.50/1.23 % (3794529)First to succeed.
% 3.50/1.23 % (3794529)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3794479"
% 3.50/1.23 % (3794530)Also succeeded, but the first one will report.
% 3.50/1.23 % (3794534)Instruction limit reached!
% 3.50/1.23 % (3794534)------------------------------
% 3.50/1.23 % (3794534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.23 % (3794534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.23 % (3794534)CaDiCaL version: 2.1.3
% 3.50/1.23 % (3794534)Termination reason: Instruction limit
% 3.50/1.23 % (3794534)Termination phase: Saturation
% 3.50/1.23 % (3794534)Time elapsed: 0.065 s
% 3.50/1.23 % (3794534)Peak memory usage: 90 MB
% 3.50/1.23 % (3794534)Instructions burned: 118 (million)
% 3.50/1.23 % (3794532)Instruction limit reached!
% 3.50/1.23 % (3794532)------------------------------
% 3.50/1.23 % (3794532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.23 % (3794532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.23 % (3794532)CaDiCaL version: 2.1.3
% 3.50/1.23 % (3794532)Termination reason: Instruction limit
% 3.50/1.23 % (3794532)Termination phase: Saturation
% 3.50/1.23 % (3794532)Time elapsed: 0.111 s
% 3.50/1.23 % (3794532)Peak memory usage: 89 MB
% 3.50/1.23 % (3794532)Instructions burned: 180 (million)
% 3.50/1.23 % (3794604)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=2269828105:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.50/1.23 % (3794605)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3966548332: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)
% 3.50/1.23 % (3794605)Also succeeded, but the first one will report.
% 3.50/1.23 % (3794529)Refutation found. Thanks to Tanya!
% 3.50/1.23 % SZS status Unsatisfiable for theBenchmark
% 3.50/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.23 % (3794529)------------------------------
% 3.50/1.23 % (3794529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.23 % (3794529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.23 % (3794529)CaDiCaL version: 2.1.3
% 3.50/1.23 % (3794529)Termination reason: Refutation
% 3.50/1.23 % (3794529)Time elapsed: 0.004 s
% 3.50/1.23 % (3794529)Peak memory usage: 88 MB
% 3.50/1.23 % (3794529)Instructions burned: 5 (million)
% 3.50/1.23 % (3794529)------------------------------
% 3.50/1.23 % (3794529)------------------------------
% 3.50/1.23 % (3794479)Success in time 0.403 s
% 3.50/1.23 % Vampire exiting
%------------------------------------------------------------------------------