%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 06:55:09 AM UTC 2026
% Result : Unsatisfiable 2.95s 0.85s
% Output : CNFRefutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 11
% Syntax : Number of formulae : 145 ( 145 unt; 0 def)
% Number of atoms : 145 ( 144 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 319 ( 44 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l1,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,multiply(VAR_1,multiply(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',l1) ).
cnf(c_1,plain,
add(A,multiply(B,multiply(A,C))) = A,
inference(clausify,[status(thm)],[l1]) ).
fof(l3,axiom,
! [VAR_0,VAR_1,VAR_2] : add(add(multiply(VAR_0,VAR_1),multiply(VAR_1,VAR_2)),VAR_1) = VAR_1,
file('theBenchmark.p',l3) ).
cnf(c_2,plain,
add(add(multiply(A,B),multiply(B,C)),B) = B,
inference(clausify,[status(thm)],[l3]) ).
fof(b1,axiom,
! [VAR_0,VAR_1] : multiply(add(VAR_0,VAR_1),add(VAR_0,inverse(VAR_1))) = VAR_0,
file('theBenchmark.p',b1) ).
cnf(c_3,plain,
multiply(add(A,B),add(A,inverse(B))) = A,
inference(clausify,[status(thm)],[b1]) ).
fof(l2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,add(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',l2) ).
cnf(c_4,plain,
multiply(A,add(B,add(A,C))) = A,
inference(clausify,[status(thm)],[l2]) ).
fof(l4,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(add(VAR_0,VAR_1),add(VAR_1,VAR_2)),VAR_1) = VAR_1,
file('theBenchmark.p',l4) ).
cnf(c_5,plain,
multiply(multiply(add(A,B),add(B,C)),B) = B,
inference(clausify,[status(thm)],[l4]) ).
fof(b2,axiom,
! [VAR_0,VAR_1] : add(multiply(VAR_0,VAR_1),multiply(VAR_0,inverse(VAR_1))) = VAR_0,
file('theBenchmark.p',b2) ).
cnf(c_6,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(clausify,[status(thm)],[b2]) ).
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_7,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(commutativity_of_multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = multiply(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_multiply) ).
cnf(c_8,plain,
multiply(A,B) = multiply(B,A),
inference(clausify,[status(thm)],[commutativity_of_multiply]) ).
fof(associativity_of_add,axiom,
! [VAR_0,VAR_1,VAR_2] : add(add(VAR_0,VAR_1),VAR_2) = add(VAR_0,add(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_add) ).
cnf(c_9,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(clausify,[status(thm)],[associativity_of_add]) ).
fof(associativity_of_multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_multiply) ).
cnf(c_10,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity_of_multiply]) ).
fof(prove_multiply_add_property,axiom,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('theBenchmark.p',prove_multiply_add_property) ).
cnf(c_11,plain,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
inference(clausify,[status(thm)],[prove_multiply_add_property]) ).
cnf(c_1797,plain,
multiply(a,add(b,c)) != add(multiply(a,b),multiply(c,a)),
inference(paramod,[status(thm)],[c_8,c_11]) ).
cnf(c_12,plain,
multiply(a,add(b,c)) != add(multiply(a,b),multiply(a,c)),
inference(paramod,[status(thm)],[c_8,c_1797]) ).
cnf(c_13,plain,
add(A,add(multiply(B,A),multiply(A,C))) = A,
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_14,plain,
multiply(A,multiply(add(B,A),add(A,C))) = A,
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_1798,plain,
add(add(A,B),multiply(C,A)) = add(A,B),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_15,plain,
add(A,add(B,multiply(C,A))) = add(A,B),
inference(paramod,[status(thm)],[c_9,c_1798]) ).
cnf(c_17,plain,
add(A,multiply(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_18,plain,
multiply(A,add(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_1799,plain,
multiply(multiply(A,B),add(C,A)) = multiply(A,B),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_21,plain,
multiply(A,multiply(B,add(C,A))) = multiply(A,B),
inference(paramod,[status(thm)],[c_10,c_1799]) ).
cnf(c_23,plain,
multiply(add(A,B),add(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_24,plain,
multiply(add(A,B),add(inverse(B),A)) = A,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_1800,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_7,c_9]) ).
cnf(c_38,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_9,c_1800]) ).
cnf(c_1801,plain,
add(multiply(A,multiply(B,C)),multiply(multiply(A,B),inverse(C))) = multiply(A,B),
inference(paramod,[status(thm)],[c_10,c_6]) ).
cnf(c_44,plain,
add(multiply(A,multiply(B,C)),multiply(A,multiply(B,inverse(C)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_10,c_1801]) ).
cnf(c_1802,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(A,C)),
inference(paramod,[status(thm)],[c_8,c_10]) ).
cnf(c_46,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)),
inference(paramod,[status(thm)],[c_10,c_1802]) ).
cnf(c_1803,plain,
add(add(A,B),add(multiply(C,add(A,B)),A)) = add(A,B),
inference(paramod,[status(thm)],[c_3,c_13]) ).
cnf(c_1804,plain,
add(add(A,B),add(A,multiply(C,add(A,B)))) = add(A,B),
inference(paramod,[status(thm)],[c_7,c_1803]) ).
cnf(c_1805,plain,
add(A,add(add(A,B),multiply(C,add(A,B)))) = add(A,B),
inference(paramod,[status(thm)],[c_38,c_1804]) ).
cnf(c_49,plain,
add(A,add(A,B)) = add(A,B),
inference(paramod,[status(thm)],[c_17,c_1805]) ).
cnf(c_1806,plain,
add(A,add(multiply(A,B),multiply(C,A))) = A,
inference(paramod,[status(thm)],[c_7,c_13]) ).
cnf(c_53,plain,
add(A,multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_15,c_1806]) ).
cnf(c_1807,plain,
multiply(A,multiply(add(B,A),A)) = A,
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_1808,plain,
multiply(A,multiply(A,add(B,A))) = A,
inference(paramod,[status(thm)],[c_8,c_1807]) ).
cnf(c_62,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_18,c_1808]) ).
cnf(c_1809,plain,
add(inverse(A),B) = add(inverse(A),multiply(B,A)),
inference(paramod,[status(thm)],[c_6,c_15]) ).
cnf(c_77,plain,
add(inverse(A),multiply(B,A)) = add(inverse(A),B),
inference(copy,[status(thm)],[c_1809]) ).
cnf(c_78,plain,
add(A,add(multiply(B,A),C)) = add(A,C),
inference(paramod,[status(thm)],[c_7,c_15]) ).
cnf(c_105,plain,
add(inverse(A),B) = add(multiply(B,A),inverse(A)),
inference(paramod,[status(thm)],[c_77,c_7]) ).
cnf(c_106,plain,
add(inverse(A),multiply(A,B)) = add(inverse(A),B),
inference(paramod,[status(thm)],[c_8,c_77]) ).
cnf(c_109,plain,
add(A,add(inverse(A),B)) = add(A,inverse(A)),
inference(paramod,[status(thm)],[c_77,c_15]) ).
cnf(c_116,plain,
add(multiply(A,B),inverse(B)) = add(A,inverse(B)),
inference(paramod,[status(thm)],[c_105,c_7]) ).
cnf(c_1810,plain,
multiply(inverse(A),B) = multiply(inverse(A),add(B,A)),
inference(paramod,[status(thm)],[c_3,c_21]) ).
cnf(c_139,plain,
multiply(inverse(A),add(B,A)) = multiply(inverse(A),B),
inference(copy,[status(thm)],[c_1810]) ).
cnf(c_1811,plain,
add(inverse(add(A,B)),A) = add(inverse(add(A,B)),add(A,inverse(B))),
inference(paramod,[status(thm)],[c_3,c_106]) ).
cnf(c_1812,plain,
add(A,inverse(add(A,B))) = add(inverse(add(A,B)),add(A,inverse(B))),
inference(paramod,[status(thm)],[c_7,c_1811]) ).
cnf(c_1813,plain,
add(A,inverse(add(A,B))) = add(add(A,inverse(B)),inverse(add(A,B))),
inference(paramod,[status(thm)],[c_7,c_1812]) ).
cnf(c_1814,plain,
add(A,inverse(add(A,B))) = add(A,add(inverse(B),inverse(add(A,B)))),
inference(paramod,[status(thm)],[c_9,c_1813]) ).
cnf(c_155,plain,
add(A,add(inverse(B),inverse(add(A,B)))) = add(A,inverse(add(A,B))),
inference(copy,[status(thm)],[c_1814]) ).
cnf(c_1815,plain,
add(inverse(A),A) = add(inverse(A),add(B,A)),
inference(paramod,[status(thm)],[c_18,c_106]) ).
cnf(c_1816,plain,
add(A,inverse(A)) = add(inverse(A),add(B,A)),
inference(paramod,[status(thm)],[c_7,c_1815]) ).
cnf(c_159,plain,
add(inverse(A),add(B,A)) = add(A,inverse(A)),
inference(copy,[status(thm)],[c_1816]) ).
cnf(c_166,plain,
add(multiply(A,B),inverse(A)) = add(B,inverse(A)),
inference(paramod,[status(thm)],[c_8,c_116]) ).
cnf(c_172,plain,
multiply(inverse(A),add(A,B)) = multiply(inverse(A),B),
inference(paramod,[status(thm)],[c_7,c_139]) ).
cnf(c_173,plain,
multiply(inverse(A),B) = multiply(add(B,A),inverse(A)),
inference(paramod,[status(thm)],[c_139,c_8]) ).
cnf(c_1817,plain,
multiply(add(multiply(A,B),A),add(B,inverse(A))) = multiply(A,B),
inference(paramod,[status(thm)],[c_166,c_3]) ).
cnf(c_1818,plain,
multiply(add(A,multiply(A,B)),add(B,inverse(A))) = multiply(A,B),
inference(paramod,[status(thm)],[c_7,c_1817]) ).
cnf(c_186,plain,
multiply(A,add(B,inverse(A))) = multiply(A,B),
inference(paramod,[status(thm)],[c_53,c_1818]) ).
cnf(c_1819,plain,
multiply(inverse(inverse(A)),add(B,inverse(A))) = multiply(inverse(inverse(A)),multiply(A,B)),
inference(paramod,[status(thm)],[c_166,c_139]) ).
cnf(c_1820,plain,
multiply(inverse(inverse(A)),B) = multiply(inverse(inverse(A)),multiply(A,B)),
inference(paramod,[status(thm)],[c_139,c_1819]) ).
cnf(c_1821,plain,
multiply(inverse(inverse(A)),B) = multiply(A,multiply(inverse(inverse(A)),B)),
inference(paramod,[status(thm)],[c_46,c_1820]) ).
cnf(c_195,plain,
multiply(A,multiply(inverse(inverse(A)),B)) = multiply(inverse(inverse(A)),B),
inference(copy,[status(thm)],[c_1821]) ).
cnf(c_200,plain,
multiply(inverse(A),B) = multiply(add(A,B),inverse(A)),
inference(paramod,[status(thm)],[c_172,c_8]) ).
cnf(c_1822,plain,
add(multiply(add(A,B),B),multiply(inverse(B),A)) = add(A,B),
inference(paramod,[status(thm)],[c_173,c_6]) ).
cnf(c_1823,plain,
add(multiply(B,add(A,B)),multiply(inverse(B),A)) = add(A,B),
inference(paramod,[status(thm)],[c_8,c_1822]) ).
cnf(c_216,plain,
add(A,multiply(inverse(A),B)) = add(B,A),
inference(paramod,[status(thm)],[c_18,c_1823]) ).
cnf(c_217,plain,
multiply(add(A,B),inverse(B)) = multiply(A,inverse(B)),
inference(paramod,[status(thm)],[c_173,c_8]) ).
cnf(c_1824,plain,
multiply(add(multiply(A,B),A),add(inverse(A),B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_106,c_24]) ).
cnf(c_1825,plain,
multiply(add(A,multiply(A,B)),add(inverse(A),B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_7,c_1824]) ).
cnf(c_247,plain,
multiply(A,add(inverse(A),B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_53,c_1825]) ).
cnf(c_259,plain,
multiply(add(A,B),inverse(A)) = multiply(B,inverse(A)),
inference(paramod,[status(thm)],[c_200,c_8]) ).
cnf(c_1826,plain,
multiply(add(A,inverse(B)),inverse(inverse(B))) = multiply(multiply(A,B),inverse(inverse(B))),
inference(paramod,[status(thm)],[c_116,c_217]) ).
cnf(c_1827,plain,
multiply(A,inverse(inverse(B))) = multiply(multiply(A,B),inverse(inverse(B))),
inference(paramod,[status(thm)],[c_217,c_1826]) ).
cnf(c_1828,plain,
multiply(A,inverse(inverse(B))) = multiply(A,multiply(B,inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_10,c_1827]) ).
cnf(c_272,plain,
multiply(A,multiply(B,inverse(inverse(B)))) = multiply(A,inverse(inverse(B))),
inference(copy,[status(thm)],[c_1828]) ).
cnf(c_1829,plain,
multiply(add(A,B),inverse(A)) = multiply(add(B,multiply(C,A)),inverse(A)),
inference(paramod,[status(thm)],[c_15,c_259]) ).
cnf(c_1830,plain,
multiply(B,inverse(A)) = multiply(add(B,multiply(C,A)),inverse(A)),
inference(paramod,[status(thm)],[c_259,c_1829]) ).
cnf(c_278,plain,
multiply(add(A,multiply(B,C)),inverse(C)) = multiply(A,inverse(C)),
inference(copy,[status(thm)],[c_1830]) ).
cnf(c_1831,plain,
multiply(add(add(inverse(A),B),A),add(inverse(A),B)) = add(inverse(A),B),
inference(paramod,[status(thm)],[c_49,c_24]) ).
cnf(c_1832,plain,
multiply(add(A,add(inverse(A),B)),add(inverse(A),B)) = add(inverse(A),B),
inference(paramod,[status(thm)],[c_7,c_1831]) ).
cnf(c_286,plain,
multiply(add(A,inverse(A)),add(inverse(A),B)) = add(inverse(A),B),
inference(paramod,[status(thm)],[c_109,c_1832]) ).
cnf(c_1833,plain,
multiply(A,add(B,inverse(A))) = multiply(A,multiply(inverse(inverse(A)),B)),
inference(paramod,[status(thm)],[c_216,c_247]) ).
cnf(c_1834,plain,
multiply(A,B) = multiply(A,multiply(inverse(inverse(A)),B)),
inference(paramod,[status(thm)],[c_186,c_1833]) ).
cnf(c_1835,plain,
multiply(A,B) = multiply(inverse(inverse(A)),B),
inference(paramod,[status(thm)],[c_195,c_1834]) ).
cnf(c_449,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(copy,[status(thm)],[c_1835]) ).
cnf(c_1836,plain,
multiply(add(A,inverse(A)),add(inverse(A),inverse(add(B,A)))) = inverse(A),
inference(paramod,[status(thm)],[c_159,c_3]) ).
cnf(c_489,plain,
add(inverse(A),inverse(add(B,A))) = inverse(A),
inference(paramod,[status(thm)],[c_286,c_1836]) ).
cnf(c_490,plain,
multiply(A,add(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_159,c_4]) ).
cnf(c_1837,plain,
multiply(inverse(inverse(A)),add(A,inverse(A))) = multiply(inverse(inverse(A)),add(B,A)),
inference(paramod,[status(thm)],[c_159,c_172]) ).
cnf(c_1838,plain,
multiply(add(A,inverse(A)),inverse(inverse(A))) = multiply(inverse(inverse(A)),add(B,A)),
inference(paramod,[status(thm)],[c_8,c_1837]) ).
cnf(c_1839,plain,
multiply(A,inverse(inverse(A))) = multiply(inverse(inverse(A)),add(B,A)),
inference(paramod,[status(thm)],[c_217,c_1838]) ).
cnf(c_1840,plain,
multiply(A,inverse(inverse(A))) = multiply(A,add(B,A)),
inference(paramod,[status(thm)],[c_449,c_1839]) ).
cnf(c_496,plain,
multiply(A,inverse(inverse(A))) = A,
inference(paramod,[status(thm)],[c_18,c_1840]) ).
cnf(c_1841,plain,
add(A,inverse(B)) = add(A,inverse(add(A,B))),
inference(paramod,[status(thm)],[c_489,c_155]) ).
cnf(c_506,plain,
add(A,inverse(add(A,B))) = add(A,inverse(B)),
inference(copy,[status(thm)],[c_1841]) ).
cnf(c_1842,plain,
multiply(A,B) = multiply(A,inverse(inverse(B))),
inference(paramod,[status(thm)],[c_496,c_272]) ).
cnf(c_507,plain,
multiply(A,inverse(inverse(B))) = multiply(A,B),
inference(copy,[status(thm)],[c_1842]) ).
cnf(c_1843,plain,
inverse(inverse(A)) = multiply(inverse(inverse(A)),A),
inference(paramod,[status(thm)],[c_490,c_139]) ).
cnf(c_1844,plain,
inverse(inverse(A)) = multiply(A,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_8,c_1843]) ).
cnf(c_1845,plain,
inverse(inverse(A)) = multiply(A,A),
inference(paramod,[status(thm)],[c_507,c_1844]) ).
cnf(c_572,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_62,c_1845]) ).
cnf(c_581,plain,
add(inverse(A),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_7,c_489]) ).
cnf(c_1846,plain,
multiply(inverse(A),add(inverse(add(A,B)),inverse(inverse(A)))) = inverse(add(A,B)),
inference(paramod,[status(thm)],[c_581,c_23]) ).
cnf(c_1847,plain,
multiply(inverse(A),add(inverse(add(A,B)),A)) = inverse(add(A,B)),
inference(paramod,[status(thm)],[c_572,c_1846]) ).
cnf(c_1848,plain,
multiply(inverse(A),add(A,inverse(add(A,B)))) = inverse(add(A,B)),
inference(paramod,[status(thm)],[c_7,c_1847]) ).
cnf(c_1849,plain,
multiply(inverse(A),add(A,inverse(B))) = inverse(add(A,B)),
inference(paramod,[status(thm)],[c_506,c_1848]) ).
cnf(c_1850,plain,
multiply(inverse(A),inverse(B)) = inverse(add(A,B)),
inference(paramod,[status(thm)],[c_172,c_1849]) ).
cnf(c_631,plain,
inverse(add(A,B)) = multiply(inverse(A),inverse(B)),
inference(copy,[status(thm)],[c_1850]) ).
cnf(c_1851,plain,
add(A,add(B,C)) = add(C,add(A,multiply(inverse(C),B))),
inference(paramod,[status(thm)],[c_216,c_38]) ).
cnf(c_688,plain,
add(A,add(B,multiply(inverse(A),C))) = add(B,add(C,A)),
inference(copy,[status(thm)],[c_1851]) ).
cnf(c_751,plain,
multiply(add(A,B),add(C,multiply(inverse(A),inverse(B)))) = multiply(add(A,B),C),
inference(paramod,[status(thm)],[c_631,c_186]) ).
cnf(c_1852,plain,
multiply(add(A,B),inverse(add(inverse(C),B))) = multiply(A,inverse(add(inverse(C),B))),
inference(paramod,[status(thm)],[c_24,c_278]) ).
cnf(c_1853,plain,
multiply(add(A,B),multiply(inverse(inverse(C)),inverse(B))) = multiply(A,inverse(add(inverse(C),B))),
inference(paramod,[status(thm)],[c_631,c_1852]) ).
cnf(c_1854,plain,
multiply(add(A,B),multiply(C,inverse(B))) = multiply(A,inverse(add(inverse(C),B))),
inference(paramod,[status(thm)],[c_572,c_1853]) ).
cnf(c_1855,plain,
multiply(add(A,B),multiply(C,inverse(B))) = multiply(A,multiply(inverse(inverse(C)),inverse(B))),
inference(paramod,[status(thm)],[c_631,c_1854]) ).
cnf(c_998,plain,
multiply(add(A,B),multiply(C,inverse(B))) = multiply(A,multiply(C,inverse(B))),
inference(paramod,[status(thm)],[c_572,c_1855]) ).
cnf(c_1856,plain,
add(A,add(multiply(B,A),multiply(inverse(A),C))) = add(C,A),
inference(paramod,[status(thm)],[c_216,c_78]) ).
cnf(c_1332,plain,
add(multiply(A,B),add(C,B)) = add(C,B),
inference(paramod,[status(thm)],[c_688,c_1856]) ).
cnf(c_1857,plain,
add(multiply(A,B),multiply(C,A)) = add(multiply(A,B),multiply(C,multiply(A,inverse(B)))),
inference(paramod,[status(thm)],[c_44,c_78]) ).
cnf(c_1344,plain,
add(multiply(A,B),multiply(C,multiply(A,inverse(B)))) = add(multiply(A,B),multiply(C,A)),
inference(copy,[status(thm)],[c_1857]) ).
cnf(c_1858,plain,
multiply(add(A,B),add(multiply(C,B),inverse(add(A,B)))) = multiply(C,B),
inference(paramod,[status(thm)],[c_1332,c_3]) ).
cnf(c_1859,plain,
multiply(add(A,B),add(multiply(C,B),multiply(inverse(A),inverse(B)))) = multiply(C,B),
inference(paramod,[status(thm)],[c_631,c_1858]) ).
cnf(c_1372,plain,
multiply(add(A,B),multiply(C,B)) = multiply(C,B),
inference(paramod,[status(thm)],[c_751,c_1859]) ).
cnf(c_1860,plain,
add(multiply(A,B),multiply(add(C,B),multiply(A,inverse(B)))) = multiply(add(C,B),A),
inference(paramod,[status(thm)],[c_1372,c_44]) ).
cnf(c_1861,plain,
add(multiply(A,B),multiply(C,multiply(A,inverse(B)))) = multiply(add(C,B),A),
inference(paramod,[status(thm)],[c_998,c_1860]) ).
cnf(c_1431,plain,
add(multiply(A,B),multiply(C,A)) = multiply(add(C,B),A),
inference(paramod,[status(thm)],[c_1344,c_1861]) ).
cnf(c_1450,plain,
add(multiply(A,B),multiply(C,A)) = multiply(A,add(C,B)),
inference(paramod,[status(thm)],[c_1431,c_8]) ).
cnf(c_1862,plain,
add(multiply(a,c),multiply(b,a)) != add(multiply(a,b),multiply(a,c)),
inference(paramod,[status(thm)],[c_1450,c_12]) ).
cnf(c_1863,plain,
add(multiply(a,c),multiply(a,b)) != add(multiply(a,b),multiply(a,c)),
inference(paramod,[status(thm)],[c_8,c_1862]) ).
cnf(c_1864,plain,
add(multiply(a,b),multiply(a,c)) != add(multiply(a,b),multiply(a,c)),
inference(paramod,[status(thm)],[c_7,c_1863]) ).
cnf(c_1796,plain,
$false,
inference(copy,[status(thm)],[c_1864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n013.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 22:37:07 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 3712296 was started by sandbox2 on n013,
% 0.15/0.43 % Sat Sep 26 22:37:07 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 2.95/0.85
% 2.95/0.85 % SZS status Unsatisfiable for theBenchmark
% 2.95/0.85
% 2.95/0.85 % Proof 1 at 0.29 (+ 0.11) seconds.
% 2.95/0.85 % Length of proof is 66.
% 2.95/0.85 % Level of proof is 16.
% 2.95/0.85 % Maximum clause weight is 53.000.
% 2.95/0.85 % Given clauses 100.
% 2.95/0.85
% 2.95/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------