%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 10:16:19 AM UTC 2026
% Result : Unsatisfiable 0.37s 0.54s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 12
% Syntax : Number of formulae : 160 ( 160 unt; 0 def)
% Number of atoms : 160 ( 159 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f6,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
fof(f9,plain,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f11,negated_conjecture,
multiply(c,inverse(a)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
fof(f12,negated_conjecture,
multiply(d,inverse(b)) = h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
fof(f13,negated_conjecture,
multiply(h,b) = j,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
fof(f14,negated_conjecture,
multiply(j,inverse(h)) = k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
fof(f15,negated_conjecture,
multiply(k,inverse(b)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
fof(f16,plain,
identity != multiply(k,inverse(b)),
inference(reorient_equations,[],[f15]) ).
fof(f31,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(multiply(X0,X0),X1)),
inference(superposition,[],[f4,f9]) ).
fof(f32,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f4,f7]) ).
fof(f33,plain,
! [X0] : multiply(c,multiply(inverse(a),X0)) = multiply(d,X0),
inference(superposition,[],[f4,f11]) ).
fof(f34,plain,
! [X0] : multiply(d,multiply(inverse(b),X0)) = multiply(h,X0),
inference(superposition,[],[f4,f12]) ).
fof(f35,plain,
! [X0] : multiply(j,multiply(inverse(h),X0)) = multiply(k,X0),
inference(superposition,[],[f4,f14]) ).
fof(f36,plain,
! [X0] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(superposition,[],[f4,f10]) ).
fof(f37,plain,
! [X0] : multiply(h,multiply(b,X0)) = multiply(j,X0),
inference(superposition,[],[f4,f13]) ).
fof(f43,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,multiply(multiply(X0,X1),multiply(X0,X1)))),
inference(superposition,[],[f9,f4]) ).
fof(f45,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))),
inference(forward_demodulation,[],[f43,f4]) ).
fof(f48,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f32,f1]) ).
fof(f49,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(X0,multiply(X0,X1))),
inference(forward_demodulation,[],[f31,f4]) ).
fof(f52,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,X1))) = X1,
inference(forward_demodulation,[],[f49,f1]) ).
fof(f55,plain,
multiply(c,multiply(b,b)) = multiply(a,identity),
inference(superposition,[],[f36,f9]) ).
fof(f56,plain,
multiply(a,identity) = multiply(c,inverse(b)),
inference(superposition,[],[f36,f7]) ).
fof(f59,plain,
a = multiply(c,inverse(b)),
inference(forward_demodulation,[],[f56,f5]) ).
fof(f60,plain,
a = multiply(c,multiply(b,b)),
inference(forward_demodulation,[],[f55,f5]) ).
fof(f63,plain,
! [X0] : multiply(c,multiply(inverse(b),X0)) = multiply(a,X0),
inference(superposition,[],[f4,f59]) ).
fof(f64,plain,
! [X0] : multiply(a,X0) = multiply(c,multiply(multiply(b,b),X0)),
inference(superposition,[],[f4,f60]) ).
fof(f65,plain,
! [X0] : multiply(a,X0) = multiply(c,multiply(b,multiply(b,X0))),
inference(forward_demodulation,[],[f64,f4]) ).
fof(f67,plain,
multiply(j,multiply(b,b)) = multiply(h,identity),
inference(superposition,[],[f37,f9]) ).
fof(f72,plain,
h = multiply(j,multiply(b,b)),
inference(forward_demodulation,[],[f67,f5]) ).
fof(f76,plain,
! [X0] : multiply(h,X0) = multiply(j,multiply(multiply(b,b),X0)),
inference(superposition,[],[f4,f72]) ).
fof(f77,plain,
! [X0] : multiply(h,X0) = multiply(j,multiply(b,multiply(b,X0))),
inference(forward_demodulation,[],[f76,f4]) ).
fof(f78,plain,
multiply(c,identity) = multiply(d,a),
inference(superposition,[],[f33,f3]) ).
fof(f81,plain,
multiply(c,identity) = multiply(d,inverse(inverse(a))),
inference(superposition,[],[f33,f7]) ).
fof(f84,plain,
c = multiply(d,inverse(inverse(a))),
inference(forward_demodulation,[],[f81,f5]) ).
fof(f87,plain,
c = multiply(d,a),
inference(forward_demodulation,[],[f78,f5]) ).
fof(f89,plain,
! [X0] : multiply(c,X0) = multiply(d,multiply(a,X0)),
inference(superposition,[],[f4,f87]) ).
fof(f90,plain,
! [X0] : multiply(c,X0) = multiply(d,multiply(inverse(inverse(a)),X0)),
inference(superposition,[],[f4,f84]) ).
fof(f94,plain,
! [X0] : multiply(c,multiply(b,X0)) = multiply(d,multiply(c,X0)),
inference(superposition,[],[f89,f36]) ).
fof(f95,plain,
multiply(d,identity) = multiply(c,multiply(a,a)),
inference(superposition,[],[f89,f9]) ).
fof(f97,plain,
multiply(c,b) = multiply(d,c),
inference(superposition,[],[f89,f10]) ).
fof(f101,plain,
d = multiply(c,multiply(a,a)),
inference(forward_demodulation,[],[f95,f5]) ).
fof(f106,plain,
! [X0] : multiply(d,X0) = multiply(c,multiply(multiply(a,a),X0)),
inference(superposition,[],[f4,f101]) ).
fof(f107,plain,
! [X0] : multiply(d,X0) = multiply(c,multiply(a,multiply(a,X0))),
inference(forward_demodulation,[],[f106,f4]) ).
fof(f108,plain,
multiply(h,b) = multiply(d,identity),
inference(superposition,[],[f34,f3]) ).
fof(f110,plain,
multiply(d,identity) = multiply(h,multiply(inverse(b),inverse(b))),
inference(superposition,[],[f34,f9]) ).
fof(f115,plain,
d = multiply(h,multiply(inverse(b),inverse(b))),
inference(forward_demodulation,[],[f110,f5]) ).
fof(f117,plain,
d = multiply(h,b),
inference(forward_demodulation,[],[f108,f5]) ).
fof(f119,plain,
d = j,
inference(superposition,[],[f117,f13]) ).
fof(f121,plain,
! [X0] : multiply(d,X0) = multiply(h,multiply(b,X0)),
inference(superposition,[],[f4,f117]) ).
fof(f124,plain,
k = multiply(d,inverse(h)),
inference(superposition,[],[f14,f119]) ).
fof(f142,plain,
! [X0] : multiply(k,X0) = multiply(d,multiply(inverse(h),X0)),
inference(forward_demodulation,[],[f35,f119]) ).
fof(f143,plain,
multiply(d,identity) = multiply(k,h),
inference(superposition,[],[f142,f3]) ).
fof(f146,plain,
multiply(d,identity) = multiply(k,inverse(inverse(h))),
inference(superposition,[],[f142,f7]) ).
fof(f149,plain,
d = multiply(k,inverse(inverse(h))),
inference(forward_demodulation,[],[f146,f5]) ).
fof(f152,plain,
d = multiply(k,h),
inference(forward_demodulation,[],[f143,f5]) ).
fof(f154,plain,
! [X0] : multiply(d,X0) = multiply(k,multiply(h,X0)),
inference(superposition,[],[f4,f152]) ).
fof(f159,plain,
! [X0] : multiply(d,multiply(b,X0)) = multiply(k,multiply(d,X0)),
inference(superposition,[],[f154,f121]) ).
fof(f162,plain,
multiply(d,multiply(inverse(b),inverse(b))) = multiply(k,d),
inference(superposition,[],[f154,f115]) ).
fof(f165,plain,
multiply(k,d) = multiply(d,b),
inference(superposition,[],[f154,f117]) ).
fof(f171,plain,
multiply(k,d) = multiply(h,inverse(b)),
inference(forward_demodulation,[],[f162,f34]) ).
fof(f180,plain,
multiply(d,b) = multiply(h,inverse(b)),
inference(forward_demodulation,[],[f171,f165]) ).
fof(f181,plain,
multiply(d,inverse(b)) = multiply(k,multiply(d,b)),
inference(superposition,[],[f154,f180]) ).
fof(f184,plain,
h = multiply(k,multiply(d,b)),
inference(forward_demodulation,[],[f181,f12]) ).
fof(f192,plain,
multiply(c,identity) = multiply(a,multiply(inverse(b),inverse(b))),
inference(superposition,[],[f63,f9]) ).
fof(f197,plain,
c = multiply(a,multiply(inverse(b),inverse(b))),
inference(forward_demodulation,[],[f192,f5]) ).
fof(f204,plain,
multiply(d,c) = multiply(c,multiply(inverse(b),inverse(b))),
inference(superposition,[],[f89,f197]) ).
fof(f207,plain,
multiply(d,c) = multiply(a,inverse(b)),
inference(forward_demodulation,[],[f204,f63]) ).
fof(f208,plain,
multiply(c,b) = multiply(a,inverse(b)),
inference(forward_demodulation,[],[f207,f97]) ).
fof(f230,plain,
! [X0] : multiply(h,X0) = multiply(d,multiply(b,multiply(b,X0))),
inference(forward_demodulation,[],[f77,f119]) ).
fof(f234,plain,
multiply(d,identity) = multiply(c,inverse(inverse(inverse(a)))),
inference(superposition,[],[f90,f7]) ).
fof(f237,plain,
d = multiply(c,inverse(inverse(inverse(a)))),
inference(forward_demodulation,[],[f234,f5]) ).
fof(f287,plain,
multiply(d,d) = multiply(c,multiply(b,inverse(a))),
inference(superposition,[],[f94,f11]) ).
fof(f290,plain,
multiply(d,d) = multiply(c,multiply(b,inverse(inverse(inverse(a))))),
inference(superposition,[],[f94,f237]) ).
fof(f291,plain,
multiply(d,identity) = multiply(c,multiply(b,inverse(c))),
inference(superposition,[],[f94,f7]) ).
fof(f296,plain,
d = multiply(c,multiply(b,inverse(c))),
inference(forward_demodulation,[],[f291,f5]) ).
fof(f309,plain,
multiply(d,d) = multiply(c,multiply(b,multiply(b,inverse(c)))),
inference(superposition,[],[f94,f296]) ).
fof(f312,plain,
multiply(d,d) = multiply(a,inverse(c)),
inference(forward_demodulation,[],[f309,f65]) ).
fof(f355,plain,
multiply(k,k) = multiply(d,multiply(b,inverse(h))),
inference(superposition,[],[f159,f124]) ).
fof(f356,plain,
multiply(k,identity) = multiply(d,multiply(b,inverse(d))),
inference(superposition,[],[f159,f7]) ).
fof(f357,plain,
multiply(k,c) = multiply(d,multiply(b,a)),
inference(superposition,[],[f159,f87]) ).
fof(f363,plain,
k = multiply(d,multiply(b,inverse(d))),
inference(forward_demodulation,[],[f356,f5]) ).
fof(f377,plain,
multiply(k,k) = multiply(d,multiply(b,multiply(b,inverse(d)))),
inference(superposition,[],[f159,f363]) ).
fof(f380,plain,
multiply(k,k) = multiply(h,inverse(d)),
inference(forward_demodulation,[],[f377,f230]) ).
fof(f441,plain,
multiply(c,multiply(a,identity)) = multiply(d,inverse(a)),
inference(superposition,[],[f107,f7]) ).
fof(f448,plain,
multiply(d,inverse(a)) = multiply(c,a),
inference(forward_demodulation,[],[f441,f5]) ).
fof(f664,plain,
multiply(d,multiply(d,d)) = multiply(c,multiply(b,multiply(b,inverse(inverse(inverse(a)))))),
inference(superposition,[],[f94,f290]) ).
fof(f667,plain,
multiply(d,multiply(d,d)) = multiply(a,inverse(inverse(inverse(a)))),
inference(forward_demodulation,[],[f664,f65]) ).
fof(f669,plain,
identity = multiply(a,inverse(inverse(inverse(a)))),
inference(forward_demodulation,[],[f667,f9]) ).
fof(f672,plain,
! [X0] : multiply(identity,X0) = multiply(a,multiply(inverse(inverse(inverse(a))),X0)),
inference(superposition,[],[f4,f669]) ).
fof(f673,plain,
! [X0] : multiply(a,multiply(inverse(inverse(inverse(a))),X0)) = X0,
inference(forward_demodulation,[],[f672,f1]) ).
fof(f676,plain,
multiply(a,identity) = inverse(inverse(a)),
inference(superposition,[],[f673,f3]) ).
fof(f686,plain,
a = inverse(inverse(a)),
inference(forward_demodulation,[],[f676,f5]) ).
fof(f696,plain,
! [X0] : multiply(a,multiply(inverse(a),X0)) = X0,
inference(superposition,[],[f673,f686]) ).
fof(f702,plain,
multiply(a,identity) = multiply(inverse(a),inverse(a)),
inference(superposition,[],[f696,f9]) ).
fof(f709,plain,
a = multiply(inverse(a),inverse(a)),
inference(forward_demodulation,[],[f702,f5]) ).
fof(f711,plain,
inverse(a) = multiply(a,a),
inference(superposition,[],[f696,f709]) ).
fof(f720,plain,
! [X0] : multiply(inverse(a),X0) = multiply(a,multiply(a,X0)),
inference(superposition,[],[f4,f711]) ).
fof(f729,plain,
! [X0] : multiply(a,multiply(inverse(a),X0)) = multiply(inverse(a),multiply(a,X0)),
inference(superposition,[],[f720,f720]) ).
fof(f753,plain,
! [X0] : multiply(inverse(a),multiply(a,X0)) = X0,
inference(forward_demodulation,[],[f729,f696]) ).
fof(f768,plain,
! [X0] : multiply(b,X0) = multiply(inverse(a),multiply(c,X0)),
inference(superposition,[],[f753,f36]) ).
fof(f778,plain,
inverse(b) = multiply(inverse(a),multiply(c,b)),
inference(superposition,[],[f753,f208]) ).
fof(f779,plain,
inverse(c) = multiply(inverse(a),multiply(d,d)),
inference(superposition,[],[f753,f312]) ).
fof(f838,plain,
multiply(inverse(a),identity) = multiply(b,multiply(c,c)),
inference(superposition,[],[f768,f9]) ).
fof(f840,plain,
! [X0] : multiply(b,multiply(b,multiply(b,X0))) = multiply(inverse(a),multiply(a,X0)),
inference(superposition,[],[f768,f65]) ).
fof(f850,plain,
multiply(b,multiply(b,inverse(a))) = multiply(inverse(a),multiply(d,d)),
inference(superposition,[],[f768,f287]) ).
fof(f860,plain,
inverse(b) = multiply(b,b),
inference(superposition,[],[f768,f778]) ).
fof(f873,plain,
inverse(c) = multiply(b,multiply(b,inverse(a))),
inference(forward_demodulation,[],[f850,f779]) ).
fof(f880,plain,
! [X0] : multiply(b,multiply(b,multiply(b,X0))) = X0,
inference(forward_demodulation,[],[f840,f753]) ).
fof(f882,plain,
inverse(a) = multiply(b,multiply(c,c)),
inference(forward_demodulation,[],[f838,f5]) ).
fof(f905,plain,
! [X0] : multiply(inverse(b),X0) = multiply(b,multiply(b,X0)),
inference(superposition,[],[f4,f860]) ).
fof(f924,plain,
multiply(d,multiply(c,c)) = multiply(h,inverse(a)),
inference(superposition,[],[f121,f882]) ).
fof(f931,plain,
multiply(c,multiply(b,c)) = multiply(h,inverse(a)),
inference(forward_demodulation,[],[f924,f94]) ).
fof(f974,plain,
multiply(c,c) = multiply(b,multiply(b,inverse(a))),
inference(superposition,[],[f880,f882]) ).
fof(f992,plain,
multiply(c,c) = inverse(c),
inference(forward_demodulation,[],[f974,f873]) ).
fof(f997,plain,
multiply(b,c) = multiply(inverse(a),inverse(c)),
inference(superposition,[],[f768,f992]) ).
fof(f1000,plain,
! [X0] : multiply(inverse(c),X0) = multiply(c,multiply(c,X0)),
inference(superposition,[],[f4,f992]) ).
fof(f1249,plain,
inverse(b) = multiply(c,multiply(c,a)),
inference(superposition,[],[f52,f59]) ).
fof(f1275,plain,
inverse(inverse(h)) = multiply(k,multiply(k,d)),
inference(superposition,[],[f52,f149]) ).
fof(f1379,plain,
inverse(inverse(h)) = multiply(k,multiply(d,b)),
inference(forward_demodulation,[],[f1275,f165]) ).
fof(f1399,plain,
inverse(b) = multiply(inverse(c),a),
inference(forward_demodulation,[],[f1249,f1000]) ).
fof(f1476,plain,
h = inverse(inverse(h)),
inference(forward_demodulation,[],[f1379,f184]) ).
fof(f1593,plain,
! [X0] : multiply(inverse(h),multiply(h,X0)) = X0,
inference(superposition,[],[f48,f1476]) ).
fof(f1681,plain,
! [X0] : multiply(b,X0) = multiply(inverse(h),multiply(d,X0)),
inference(superposition,[],[f1593,f121]) ).
fof(f1695,plain,
inverse(d) = multiply(inverse(h),multiply(k,k)),
inference(superposition,[],[f1593,f380]) ).
fof(f1815,plain,
multiply(inverse(h),identity) = multiply(b,multiply(d,d)),
inference(superposition,[],[f1681,f9]) ).
fof(f1832,plain,
multiply(b,multiply(b,inverse(h))) = multiply(inverse(h),multiply(k,k)),
inference(superposition,[],[f1681,f355]) ).
fof(f1873,plain,
inverse(d) = multiply(b,multiply(b,inverse(h))),
inference(forward_demodulation,[],[f1832,f1695]) ).
fof(f1887,plain,
inverse(h) = multiply(b,multiply(d,d)),
inference(forward_demodulation,[],[f1815,f5]) ).
fof(f1898,plain,
inverse(d) = multiply(inverse(b),inverse(h)),
inference(forward_demodulation,[],[f1873,f905]) ).
fof(f1961,plain,
multiply(d,d) = multiply(b,multiply(b,inverse(h))),
inference(superposition,[],[f52,f1887]) ).
fof(f1964,plain,
multiply(d,d) = multiply(inverse(b),inverse(h)),
inference(forward_demodulation,[],[f1961,f905]) ).
fof(f2015,plain,
multiply(d,d) = inverse(d),
inference(forward_demodulation,[],[f1964,f1898]) ).
fof(f2017,plain,
inverse(c) = multiply(inverse(a),inverse(d)),
inference(superposition,[],[f779,f2015]) ).
fof(f2024,plain,
! [X0] : multiply(d,multiply(d,X0)) = multiply(inverse(d),X0),
inference(superposition,[],[f4,f2015]) ).
fof(f2026,plain,
multiply(a,inverse(c)) = inverse(d),
inference(superposition,[],[f696,f2017]) ).
fof(f2036,plain,
multiply(inverse(a),inverse(c)) = multiply(a,inverse(d)),
inference(superposition,[],[f720,f2026]) ).
fof(f2044,plain,
multiply(b,c) = multiply(a,inverse(d)),
inference(forward_demodulation,[],[f2036,f997]) ).
fof(f2820,plain,
identity = multiply(d,multiply(inverse(a),multiply(d,multiply(inverse(a),multiply(c,a))))),
inference(superposition,[],[f45,f448]) ).
fof(f3392,plain,
identity = multiply(d,multiply(inverse(a),multiply(d,multiply(b,a)))),
inference(forward_demodulation,[],[f2820,f768]) ).
fof(f3716,plain,
identity = multiply(d,multiply(inverse(a),multiply(k,c))),
inference(forward_demodulation,[],[f3392,f357]) ).
fof(f4351,plain,
multiply(d,multiply(d,identity)) = multiply(inverse(a),multiply(k,c)),
inference(superposition,[],[f52,f3716]) ).
fof(f4354,plain,
multiply(inverse(d),identity) = multiply(inverse(a),multiply(k,c)),
inference(forward_demodulation,[],[f4351,f2024]) ).
fof(f4361,plain,
inverse(d) = multiply(inverse(a),multiply(k,c)),
inference(forward_demodulation,[],[f4354,f5]) ).
fof(f4372,plain,
multiply(k,c) = multiply(a,inverse(d)),
inference(superposition,[],[f48,f4361]) ).
fof(f4379,plain,
multiply(k,c) = multiply(b,c),
inference(forward_demodulation,[],[f4372,f2044]) ).
fof(f4392,plain,
identity = multiply(k,multiply(c,multiply(k,multiply(c,multiply(b,c))))),
inference(superposition,[],[f45,f4379]) ).
fof(f4396,plain,
identity = multiply(k,multiply(c,multiply(k,multiply(h,inverse(a))))),
inference(forward_demodulation,[],[f4392,f931]) ).
fof(f4398,plain,
identity = multiply(k,multiply(c,multiply(d,inverse(a)))),
inference(forward_demodulation,[],[f4396,f154]) ).
fof(f4399,plain,
identity = multiply(k,multiply(c,multiply(c,a))),
inference(forward_demodulation,[],[f4398,f448]) ).
fof(f4400,plain,
identity = multiply(k,multiply(inverse(c),a)),
inference(forward_demodulation,[],[f4399,f1000]) ).
fof(f4401,plain,
identity = multiply(k,inverse(b)),
inference(forward_demodulation,[],[f4400,f1399]) ).
fof(f4402,plain,
$false,
inference(forward_subsumption_resolution,[],[f4401,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:15:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.54 % (2557911)Will run a generic schedule for satisfiability detection.
% 0.37/0.54 % (2557919)dis+10_1_sil=32000:sp=arity:random_seed=1968263464:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.37/0.54 % (2557917)% WARNING: option uhcvi not known.
% 0.37/0.54 % (2557916)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=646129847_2999 on theBenchmark for (2999ds/0Mi)
% 0.37/0.54 % (2557920)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3035003760:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.37/0.54 % (2557918)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4010861466:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.37/0.54 % (2557922)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=11628080:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.37/0.54 % (2557921)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1871730495:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.37/0.54 % (2557917)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3570865635:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.37/0.54 % TRYING [1]
% 0.37/0.54 % TRYING [2]
% 0.37/0.54 % TRYING [3]
% 0.37/0.54 % TRYING [4]
% 0.37/0.54 % TRYING [5]
% 0.37/0.54 % TRYING [6]
% 0.37/0.54 % (2557919)Instruction limit reached!
% 0.37/0.54 % (2557919)------------------------------
% 0.37/0.54 % (2557919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.54 % (2557919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.54 % (2557919)CaDiCaL version: 2.1.3
% 0.37/0.54 % (2557919)Termination reason: Instruction limit
% 0.37/0.54 % (2557919)Termination phase: Saturation
% 0.37/0.54 % (2557919)Time elapsed: 0.031 s
% 0.37/0.54 % (2557919)Peak memory usage: 12 MB
% 0.37/0.54 % (2557919)Instructions burned: 104 (million)
% 0.37/0.54 % (2557930)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2389089069:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.37/0.54 % TRYING [1]
% 0.37/0.54 % TRYING [2]
% 0.37/0.54 % TRYING [3]
% 0.37/0.54 % TRYING [4]
% 0.37/0.54 % TRYING [5]
% 0.37/0.54 % TRYING [7]
% 0.37/0.54 % TRYING [6]
% 0.37/0.54 % (2557920)Instruction limit reached!
% 0.37/0.54 % (2557920)------------------------------
% 0.37/0.54 % (2557920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.54 % (2557920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.54 % (2557920)CaDiCaL version: 2.1.3
% 0.37/0.54 % (2557920)Termination reason: Instruction limit
% 0.37/0.54 % (2557920)Termination phase: Saturation
% 0.37/0.54 % (2557920)Time elapsed: 0.063 s
% 0.37/0.54 % (2557920)Peak memory usage: 12 MB
% 0.37/0.54 % (2557920)Instructions burned: 116 (million)
% 0.37/0.54 % (2557921)Instruction limit reached!
% 0.37/0.54 % (2557921)------------------------------
% 0.37/0.54 % (2557921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.54 % (2557921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.54 % (2557921)CaDiCaL version: 2.1.3
% 0.37/0.54 % (2557921)Termination reason: Instruction limit
% 0.37/0.54 % (2557921)Termination phase: Saturation
% 0.37/0.54 % (2557921)Time elapsed: 0.070 s
% 0.37/0.54 % (2557921)Peak memory usage: 12 MB
% 0.37/0.54 % (2557921)Instructions burned: 133 (million)
% 0.37/0.54 % TRYING [7]
% 0.37/0.54 % (2557932)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=669570504:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.37/0.54 % (2557918) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2557911-2557918"...
% 0.37/0.54 % (2557933)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1781089892:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.37/0.54 % (2557918)...printing done.
% 0.37/0.54 % (2557918)Refutation found. Thanks to Tanya!
% 0.37/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.37/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.54 % (2557918)------------------------------
% 0.37/0.54 % (2557918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.54 % (2557918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.54 % (2557918)CaDiCaL version: 2.1.3
% 0.37/0.54 % (2557918)Termination reason: Refutation
% 0.37/0.54 % (2557918)Time elapsed: 0.090 s
% 0.37/0.54 % (2557918)Peak memory usage: 13 MB
% 0.37/0.54 % (2557918)Instructions burned: 168 (million)
% 0.37/0.54 % (2557911)Success in time 0.126 s
% 0.37/0.54 % Vampire exiting
%------------------------------------------------------------------------------