%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP043-2 : 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 10:12:14 AM UTC 2026
% Result : Unsatisfiable 3.75s 1.52s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ equalish(X0,X1)
| ~ product(X2,X3,X0)
| product(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
fof(f8,axiom,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
fof(f9,axiom,
equalish(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_equals_c) ).
fof(f10,negated_conjecture,
~ equalish(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity) ).
fof(f11,plain,
! [X0,X1] :
( ~ product(X0,X1,c)
| ~ product(X0,X1,a) ),
inference(resolution,[],[f4,f10]) ).
fof(f13,plain,
! [X0,X1] :
( product(X0,X1,b)
| ~ product(X0,X1,a) ),
inference(resolution,[],[f7,f8]) ).
fof(f14,plain,
! [X0,X1] :
( product(X0,X1,c)
| ~ product(X0,X1,b) ),
inference(resolution,[],[f7,f9]) ).
fof(f39,plain,
! [X0,X1] :
( ~ product(X0,X1,b)
| ~ product(X0,X1,a) ),
inference(resolution,[],[f14,f11]) ).
fof(f43,plain,
! [X0,X1] :
( ~ product(X0,X1,a)
| ~ product(X0,X1,a) ),
inference(resolution,[],[f39,f13]) ).
fof(f46,plain,
! [X0,X1] : ~ product(X0,X1,a),
inference(duplicate_literal_removal,[],[f43]) ).
fof(f88,plain,
$false,
inference(resolution,[],[f46,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n009.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 09:16:15 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 3.75/1.52 % (1760213)Input is clausal, will run a generic CNF schedule.
% 3.75/1.52 % (1760222)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3182655504:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.75/1.52 % (1760222)Instruction limit reached!
% 3.75/1.52 % (1760222)------------------------------
% 3.75/1.52 % (1760222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.52 % (1760222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.52 % (1760222)CaDiCaL version: 2.1.3
% 3.75/1.52 % (1760222)Termination reason: Instruction limit
% 3.75/1.52 % (1760222)Termination phase: Saturation
% 3.75/1.52 % (1760222)Time elapsed: 0.032 s
% 3.75/1.52 % (1760222)Peak memory usage: 87 MB
% 3.75/1.52 % (1760222)Instructions burned: 119 (million)
% 3.75/1.52 % (1760223)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2041280143:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.75/1.52 % (1760220)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1847620355:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.75/1.52 % (1760224)dis-21_1_sil=8000:lcm=predicate:random_seed=1457240294: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)
% 3.75/1.52 % (1760218)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=827114668:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.75/1.52 % (1760221)lrs+10_1_sil=8000:sp=occurrence:random_seed=619317179:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.75/1.52 % (1760219)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3259068306:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.75/1.52 % (1760224)First to succeed.
% 3.75/1.52 % (1760224)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1760213"
% 3.75/1.52 % (1760223)Also succeeded, but the first one will report.
% 3.75/1.52 % (1760221)Also succeeded, but the first one will report.
% 3.75/1.52 % (1760226)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=32364306:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.75/1.52 % (1760226)Refutation not found, incomplete strategy
% 3.75/1.52 % (1760226)------------------------------
% 3.75/1.52 % (1760226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.52 % (1760226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.52 % (1760226)CaDiCaL version: 2.1.3
% 3.75/1.52 % (1760226)Termination reason: Refutation not found, incomplete strategy
% 3.75/1.52 % (1760226)Time elapsed: 0.001 s
% 3.75/1.52 % (1760226)Peak memory usage: 87 MB
% 3.75/1.52 % (1760224)Refutation found. Thanks to Tanya!
% 3.75/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.75/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.52 % (1760224)------------------------------
% 3.75/1.52 % (1760224)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.52 % (1760224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.52 % (1760224)CaDiCaL version: 2.1.3
% 3.75/1.52 % (1760224)Termination reason: Refutation
% 3.75/1.52 % (1760224)Time elapsed: 0.003 s
% 3.75/1.52 % (1760224)Peak memory usage: 88 MB
% 3.75/1.52 % (1760224)Instructions burned: 3 (million)
% 3.75/1.52 % (1760224)------------------------------
% 3.75/1.52 % (1760224)------------------------------
% 3.75/1.52 % (1760213)Success in time 0.436 s
% 3.75/1.52 % Vampire exiting
%------------------------------------------------------------------------------