%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP044-2 : 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 : n004.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 3.99s 1.52s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 32 ( 19 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
fof(f8,axiom,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
fof(f9,axiom,
product(a,c,result),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_with_a) ).
fof(f10,negated_conjecture,
~ product(b,c,result),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_with_b) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,b)
| ~ product(X2,X1,result)
| ~ product(X0,c,X1) ),
inference(resolution,[],[f6,f10]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ equalish(X3,b)
| ~ product(X2,c,X1)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,result) ),
inference(resolution,[],[f27,f7]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,a)
| ~ product(X0,c,X1)
| ~ product(X2,X1,result) ),
inference(resolution,[],[f34,f8]) ).
fof(f139,plain,
! [X0] :
( ~ product(identity,X0,result)
| ~ product(a,c,X0) ),
inference(resolution,[],[f66,f1]) ).
fof(f461,plain,
~ product(a,c,result),
inference(resolution,[],[f139,f1]) ).
fof(f465,plain,
$false,
inference(forward_subsumption_resolution,[],[f461,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP044-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:16:07 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.99/1.52 % (3237125)Input is clausal, will run a generic CNF schedule.
% 3.99/1.52 % (3237219)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=43975390:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.99/1.52 % (3237216)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=561443552:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.99/1.52 % (3237215)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=1085627726:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.99/1.52 % (3237217)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3339305866:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.99/1.52 % (3237218)lrs+10_1_sil=8000:sp=occurrence:random_seed=883146305:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.99/1.52 % (3237219)Instruction limit reached!
% 3.99/1.52 % (3237219)------------------------------
% 3.99/1.52 % (3237219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.52 % (3237219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.52 % (3237219)CaDiCaL version: 2.1.3
% 3.99/1.52 % (3237219)Termination reason: Instruction limit
% 3.99/1.52 % (3237219)Termination phase: Saturation
% 3.99/1.52 % (3237219)Time elapsed: 0.034 s
% 3.99/1.52 % (3237219)Peak memory usage: 88 MB
% 3.99/1.52 % (3237219)Instructions burned: 117 (million)
% 3.99/1.52 % (3237218)Refutation not found, incomplete strategy
% 3.99/1.52 % (3237218)------------------------------
% 3.99/1.52 % (3237218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.52 % (3237218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.52 % (3237218)CaDiCaL version: 2.1.3
% 3.99/1.52 % (3237218)Termination reason: Refutation not found, incomplete strategy
% 3.99/1.52 % (3237218)Time elapsed: 0.002 s
% 3.99/1.52 % (3237218)Peak memory usage: 88 MB
% 3.99/1.52 % (3237218)Instructions burned: 1 (million)
% 3.99/1.52 % (3237221)dis-21_1_sil=8000:lcm=predicate:random_seed=2019363254: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)
% 3.99/1.52 % (3237220)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=781695308:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.99/1.52 % (3237220)First to succeed.
% 3.99/1.52 % (3237220)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3237125"
% 3.99/1.52 % (3237221)Also succeeded, but the first one will report.
% 3.99/1.52 % (3237250)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=1805755424:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.99/1.52 % (3237250)Instruction limit reached!
% 3.99/1.52 % (3237250)------------------------------
% 3.99/1.52 % (3237250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.52 % (3237250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.52 % (3237250)CaDiCaL version: 2.1.3
% 3.99/1.52 % (3237250)Termination reason: Instruction limit
% 3.99/1.52 % (3237250)Termination phase: Saturation
% 3.99/1.52 % (3237250)Time elapsed: 0.051 s
% 3.99/1.52 % (3237250)Peak memory usage: 89 MB
% 3.99/1.52 % (3237250)Instructions burned: 144 (million)
% 3.99/1.52 % (3237218)------------------------------
% 3.99/1.52 % (3237218)------------------------------
% 3.99/1.52 % (3237220)Refutation found. Thanks to Tanya!
% 3.99/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.99/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.99/1.52 % (3237220)------------------------------
% 3.99/1.52 % (3237220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.52 % (3237220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.52 % (3237220)CaDiCaL version: 2.1.3
% 3.99/1.52 % (3237220)Termination reason: Refutation
% 3.99/1.52 % (3237220)Time elapsed: 0.017 s
% 3.99/1.52 % (3237220)Peak memory usage: 88 MB
% 3.99/1.52 % (3237220)Instructions burned: 24 (million)
% 3.99/1.52 % (3237220)------------------------------
% 3.99/1.52 % (3237220)------------------------------
% 3.99/1.52 % (3237125)Success in time 0.478 s
% 3.99/1.52 % Vampire exiting
%------------------------------------------------------------------------------