%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP113-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 10:16:41 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.50s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 27 ( 17 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 33 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f6,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0] :
( X0 = a
| X0 = b
| X0 = c
| X0 = identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_of_group1) ).
fof(f9,plain,
! [X0] :
( a = X0
| b = X0
| c = X0
| identity = X0 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_b) ).
fof(f11,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
fof(f12,axiom,
a != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_identity) ).
fof(f13,plain,
identity != a,
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_c) ).
fof(f15,axiom,
b != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_identity) ).
fof(f16,plain,
identity != b,
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
c != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_identity) ).
fof(f18,plain,
identity != c,
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(a,a) != identity
| multiply(b,b) != identity
| multiply(c,c) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_identity) ).
fof(f20,plain,
( identity != multiply(a,a)
| identity != multiply(b,b)
| identity != multiply(c,c) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(a,a) != b
| multiply(a,multiply(a,a)) != c
| multiply(a,multiply(a,multiply(a,a))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_a) ).
fof(f22,plain,
( b != multiply(a,a)
| c != multiply(a,multiply(a,a))
| identity != multiply(a,multiply(a,multiply(a,a))) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(b,b) != c
| multiply(b,multiply(b,b)) != a
| multiply(b,multiply(b,multiply(b,b))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_b) ).
fof(f24,plain,
( c != multiply(b,b)
| a != multiply(b,multiply(b,b))
| identity != multiply(b,multiply(b,multiply(b,b))) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(c,c) != a
| multiply(c,multiply(c,c)) != b
| multiply(c,multiply(c,multiply(c,c))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_c) ).
fof(f26,plain,
( a != multiply(c,c)
| b != multiply(c,multiply(c,c))
| identity != multiply(c,multiply(c,multiply(c,c))) ),
inference(reorient_equations,[],[f25]) ).
fof(f106,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f1,f3,f4,f5,f7,f9,f10,f11,f13,f14,f16,f18,f20,f22,f24,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP113-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/5.42 % Computer : n003.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Sun Sep 27 09:21:31 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/5.45 Running first-order model finding
% 0.14/5.45 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.50 % (241681)Will run a generic schedule for satisfiability detection.
% 0.14/5.50 % (241686)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2890056441_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/5.50 % Detected minimum model sizes of [4]
% 0.14/5.50 % Detected maximum model sizes of [4]
% 0.14/5.50 % TRYING [4]
% 0.14/5.50 % (241687)% WARNING: option uhcvi not known.
% 0.14/5.50 % (241686) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-241681-241686"...
% 0.14/5.50 % (241686)...printing done.
% 0.14/5.50 % (241686)Refutation found. Thanks to Tanya!
% 0.14/5.50 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/5.50 % (241686)------------------------------
% 0.14/5.50 % (241686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/5.50 % (241686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/5.50 % (241686)CaDiCaL version: 2.1.3
% 0.14/5.50 % (241686)Termination reason: Refutation
% 0.14/5.50 % (241686)Time elapsed: 0.004 s
% 0.14/5.50 % (241686)Peak memory usage: 11 MB
% 0.14/5.50 % (241686)Instructions burned: 14 (million)
% 0.14/5.50 % (241681)Success in time 0.033 s
% 0.14/5.50 % Vampire exiting
%------------------------------------------------------------------------------