%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 06:45:52 AM UTC 2026
% Result : Unsatisfiable 32.04s 8.56s
% Output : Refutation 27.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 95 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 163 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 757 ( 106 ~; 69 |; 0 &; 582 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 148 ( 0 ^; 148 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ difference ) @ difference ) )
= ( C @ ( B @ difference ) @ ( C @ ( A @ difference ) @ difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ difference ) @ difference ) )
= ( C @ ( B @ difference ) @ ( C @ ( A @ difference ) @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ difference ) @ difference ) )
= ( C @ ( B @ difference ) @ ( C @ ( A @ difference ) @ difference ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ difference ) )
= ( A @ ( B @ difference ) @ ( B @ difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_2) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ difference ) )
= ( A @ ( B @ difference ) @ ( B @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ difference ) )
= ( A @ ( B @ difference ) @ ( B @ difference ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( B @ ( A @ difference ) @ ( A @ difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( B @ ( A @ difference ) @ ( A @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ difference ) )
= ( B @ ( A @ multiply ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( A @ ( B @ multiply ) ) ),
inference(rewrite,[status(thm)],[12,16]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( A @ difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_1) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( A @ difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( A @ difference ) )
= A ),
inference(lifteq,[status(thm)],[9]) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ difference ) @ ( A @ difference ) )
!= ( D @ ( C @ difference ) ) )
| ( ( A @ ( C @ difference ) )
= ( D @ ( C @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,16]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ difference ) )
= ( B @ ( A @ difference ) @ ( B @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ difference ) ))]]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ difference ) )
= ( B @ ( A @ difference ) @ ( B @ multiply ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) @ ( B @ multiply ) )
!= ( D @ ( C @ multiply ) ) )
| ( ( B @ ( B @ difference ) )
= ( C @ ( D @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,62]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ difference ) )
= ( B @ ( B @ ( A @ difference ) @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ difference ) ))]]) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ difference ) )
= ( B @ ( B @ ( A @ difference ) @ multiply ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( D @ ( D @ ( C @ difference ) @ multiply ) ) )
| ( ( A @ ( B @ multiply ) )
= ( D @ ( D @ difference ) ) ) ),
inference(paramod_ordered,[status(thm)],[62,304]) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( A @ multiply ) )
= ( A @ ( A @ difference ) ) ),
inference(pattern_uni,[status(thm)],[503:[bind(A,$thf( B @ ( E @ difference ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(591,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( A @ multiply ) )
= ( A @ ( A @ difference ) ) ),
inference(simp,[status(thm)],[504]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) @ ( A @ difference ) )
!= ( C @ ( D @ difference ) @ ( C @ difference ) ) )
| ( ( B @ ( A @ multiply ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[16,10]) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( A @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B ))]]) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ multiply ) )
= A ),
inference(simp,[status(thm)],[24]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ ( a @ multiply ) @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
thf(6,plain,
( ( c @ ( b @ ( a @ multiply ) @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
( ( c @ ( b @ ( a @ multiply ) @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( c @ ( b @ ( a @ multiply ) @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( ( c @ ( A @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,8]) ).
thf(41,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( ( c @ ( A @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(44,plain,
( ( b != a )
| ( ( c @ ( b @ multiply ) @ ( a @ multiply ) )
!= ( c @ ( a @ multiply ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(36,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( c @ ( b @ ( a @ multiply ) @ multiply ) ) )
| ( A
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,8]) ).
thf(39,plain,
( ( ( c @ ( b @ multiply ) @ ( a @ multiply ) )
!= c )
| ( ( c @ ( b @ multiply ) @ ( a @ multiply ) )
!= ( b @ ( a @ multiply ) ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( c @ ( b @ ( a @ multiply ) @ multiply ) ) )
| ( ( A @ ( B @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[62,8]) ).
thf(66,plain,
( ( b @ ( a @ multiply ) @ ( c @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( b @ ( a @ multiply ) )),bind(B,$thf( c ))]]) ).
thf(91,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( ( A @ ( c @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,66]) ).
thf(94,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( ( A @ ( c @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(99,plain,
( ( b != a )
| ( ( a @ ( c @ multiply ) )
!= ( c @ ( b @ multiply ) @ ( a @ multiply ) ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) @ ( A @ difference ) )
!= ( D @ ( C @ difference ) ) )
| ( ( B @ ( A @ multiply ) @ ( C @ difference ) )
= ( D @ ( C @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,16]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( A @ difference ) )
= ( B @ ( A @ difference ) @ ( A @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ difference ) ))]]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( A @ difference ) )
= ( B @ ( A @ difference ) @ ( A @ multiply ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(631,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( B @ difference ) )
= ( C @ ( B @ difference ) @ ( B @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,31]) ).
thf(632,plain,
! [A: $i] :
( ( A @ ( A @ difference ) @ ( A @ multiply ) )
= ( A @ ( A @ difference ) ) ),
inference(pattern_uni,[status(thm)],[631:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ difference ) @ ( A @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( A @ difference ) )
= ( B @ ( C @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[632,62]) ).
thf(1240,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ difference ) @ multiply ) )
= ( A @ ( A @ difference ) ) ),
inference(pattern_uni,[status(thm)],[1239:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ difference ) ))]]) ).
thf(1314,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ difference ) @ multiply ) )
= ( A @ ( A @ difference ) ) ),
inference(simp,[status(thm)],[1240]) ).
thf(229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ difference ) )
!= ( C @ ( D @ difference ) ) )
| ( ( B @ ( A @ difference ) @ ( B @ multiply ) @ ( C @ difference ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[35,10]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( B @ multiply ) @ ( B @ difference ) )
= B ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B ))]]) ).
thf(595,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( B @ difference ) @ ( B @ multiply ) )
= B ),
inference(rewrite,[status(thm)],[230,31]) ).
thf(1116,plain,
! [A: $i] :
( ( A @ ( A @ multiply ) )
= A ),
inference(rewrite,[status(thm)],[595,10]) ).
thf(1548,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( ( c @ ( b @ multiply ) @ ( a @ multiply ) )
!= c )
| ( ( A @ ( a @ multiply ) )
!= ( b @ ( a @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[1116,39]) ).
thf(1566,plain,
! [A: $i] :
( ( A != c )
| ( A != b )
| ( ( c @ ( b @ multiply ) @ ( a @ multiply ) )
!= c )
| ( A != b )
| ( a != a ) ),
inference(simp,[status(thm)],[1548]) ).
thf(1640,plain,
( ( c != b )
| ( ( c @ ( b @ multiply ) @ ( a @ multiply ) )
!= c ) ),
inference(simp,[status(thm)],[1566]) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ difference ) @ ( A @ difference ) )
!= ( C @ ( D @ difference ) ) )
| ( ( A @ ( C @ difference ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[10,10]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ difference ) @ difference ) )
= ( B @ ( A @ difference ) ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ difference ) )),bind(D,$thf( F ))]]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ difference ) @ difference ) )
= ( B @ ( A @ difference ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(17,plain,
( ( ( c @ ( b @ multiply ) )
!= c )
| ( ( b @ ( a @ multiply ) )
!= a ) ),
inference(simp,[status(thm)],[8]) ).
thf(51,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( A != c )
| ( ( b @ ( a @ multiply ) )
!= a ) ),
inference(paramod_ordered,[status(thm)],[32,17]) ).
thf(55,plain,
( ( c != c )
| ( c != b )
| ( ( b @ ( a @ multiply ) )
!= a ) ),
inference(simp,[status(thm)],[51]) ).
thf(57,plain,
( ( c != b )
| ( ( b @ ( a @ multiply ) )
!= a ) ),
inference(simp,[status(thm)],[55]) ).
thf(2059,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( c != b )
| ( ( A @ ( a @ multiply ) )
!= c ) ),
inference(paramod_ordered,[status(thm)],[1116,1640]) ).
thf(2080,plain,
! [A: $i] :
( ( A != c )
| ( A != b )
| ( c != b )
| ( ( A @ ( a @ multiply ) )
!= c ) ),
inference(simp,[status(thm)],[2059]) ).
thf(2083,plain,
( ( c != b )
| ( ( b @ ( a @ multiply ) )
!= c ) ),
inference(simp,[status(thm)],[2080]) ).
thf(446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ difference ) )
!= ( C @ ( D @ difference ) ) )
| ( ( B @ ( B @ ( A @ difference ) @ multiply ) @ ( C @ difference ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[304,10]) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ difference ) @ multiply ) @ ( B @ difference ) )
= B ),
inference(pattern_uni,[status(thm)],[446:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B ))]]) ).
thf(710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= ( D @ ( D @ ( C @ difference ) @ multiply ) ) )
| ( ( A @ ( B @ multiply ) @ ( D @ difference ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[62,447]) ).
thf(711,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( A @ multiply ) @ ( A @ difference ) )
= A ),
inference(pattern_uni,[status(thm)],[710:[bind(A,$thf( B @ ( E @ difference ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(749,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( A @ multiply ) @ ( A @ difference ) )
= A ),
inference(simp,[status(thm)],[711]) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ difference ) @ ( A @ difference ) @ ( A @ multiply ) )
= A ),
inference(rewrite,[status(thm)],[749,31]) ).
thf(1381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) @ ( A @ difference ) )
!= ( C @ ( D @ difference ) @ ( C @ difference ) ) )
| ( ( B @ ( A @ multiply ) @ ( C @ multiply ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[16,1332]) ).
thf(1382,plain,
! [A: $i] :
( ( A @ ( A @ multiply ) @ ( A @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[1381:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B ))]]) ).
thf(1502,plain,
! [A: $i] :
( ( A @ ( A @ multiply ) @ ( A @ multiply ) )
= A ),
inference(simp,[status(thm)],[1382]) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) @ ( A @ difference ) )
!= ( C @ ( D @ difference ) ) )
| ( ( B @ ( A @ multiply ) @ ( C @ difference ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[16,10]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ ( A @ difference ) @ difference ) )
= ( B @ ( A @ difference ) ) ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ difference ) )),bind(D,$thf( E ))]]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ ( A @ difference ) @ difference ) )
= ( B @ ( A @ difference ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(954,plain,
( ( b != a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ( c != a ) ),
inference(simp,[status(thm)],[99]) ).
thf(976,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( b != a )
| ( A != a )
| ( c != a ) ),
inference(paramod_ordered,[status(thm)],[32,954]) ).
thf(981,plain,
( ( c != a )
| ( b != a )
| ( b != a )
| ( c != a ) ),
inference(simp,[status(thm)],[976]) ).
thf(985,plain,
( ( b != a )
| ( c != a ) ),
inference(simp,[status(thm)],[981]) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( A @ ( C @ ( B @ difference ) @ difference ) )
= ( C @ ( B @ difference ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,33]) ).
thf(1050,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ difference ) @ difference ) )
= ( A @ ( A @ difference ) ) ),
inference(pattern_uni,[status(thm)],[1049:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(42,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( ( c @ ( b @ multiply ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[37]) ).
thf(45,plain,
( ( b != a )
| ( ( c @ ( b @ multiply ) )
!= c ) ),
inference(simp,[status(thm)],[42]) ).
thf(46,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( b != a )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[32,45]) ).
thf(48,plain,
( ( c != c )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[46]) ).
thf(49,plain,
( ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[48]) ).
thf(86,plain,
( ( ( c @ ( b @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( c != a ) ),
inference(simp,[status(thm)],[66]) ).
thf(1713,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ multiply ) @ ( A @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( A
= ( B @ ( C @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[1502,62]) ).
thf(1714,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ multiply ) @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[1713:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ multiply ) ))]]) ).
thf(1821,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ multiply ) @ multiply ) )
= A ),
inference(simp,[status(thm)],[1714]) ).
thf(2245,plain,
! [A: $i] :
( ( ( A @ ( A @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( c != b )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[1116,2083]) ).
thf(2250,plain,
( ( c != b )
| ( c != a )
| ( c != b ) ),
inference(simp,[status(thm)],[2245]) ).
thf(2262,plain,
( ( c != a )
| ( c != b ) ),
inference(simp,[status(thm)],[2250]) ).
thf(4649,plain,
$false,
inference(e,[status(thm)],[14,591,9,44,39,35,11,99,8,1314,10,1640,20,57,6,2083,1502,33,985,1050,13,32,45,17,1332,49,86,1821,66,16,31,304,632,2262,1116,447,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.25/0.49 % Computer : n008.cluster.edu
% 0.25/0.49 % Model : x86_64 x86_64
% 0.25/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.49 % Memory : 8046.5625MB
% 0.25/0.49 % OS : Linux 6.8.0-71-generic
% 0.25/0.49 % CPULimit : 300
% 0.25/0.49 % WCLimit : 300
% 0.25/0.49 % DateTime : Sat Sep 26 20:58:09 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.43/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.78/1.59 % [INFO] Parsing done (251ms).
% 1.96/1.62 % [INFO] Running in sequential loop mode.
% 2.87/2.23 % [INFO] eprover registered as external prover.
% 2.87/2.24 % [INFO] Scanning for conjecture ...
% 3.04/2.35 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.21/2.40 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.21/2.42 % [INFO] Problem is propositional (TPTP CNF).
% 3.21/2.43 % [INFO] Type checking passed.
% 3.21/2.44 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 32.04/8.55 % External prover 'e' found a proof!
% 32.04/8.55 % [INFO] Killing All external provers ...
% 32.04/8.55 % Time passed: 7851ms (effective reasoning time: 6925ms)
% 32.04/8.55 % Axioms used in derivation (4): set_difference_3, set_difference_2, intersection, set_difference_1
% 32.04/8.55 % No. of inferences in proof: 95
% 32.04/8.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7851 ms resp. 6925 ms w/o parsing
% 27.04/8.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.04/8.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------