%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 08:08:04 AM UTC 2026
% Result : Unsatisfiable 9.39s 5.29s
% Output : Refutation 8.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 108 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 275 ( 93 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1452 ( 171 ~; 99 |; 0 &;1182 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 216 ( 0 ^; 216 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(subtract_decl,type,
subtract: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ subtract ) @ add ) @ ( C @ ( B @ ( A @ add ) @ subtract ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity2) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ subtract ) @ add ) @ ( C @ ( B @ ( A @ add ) @ subtract ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(1,negated_conjecture,
~ ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(14,plain,
~ ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(15,plain,
~ ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[18,15]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
! [A: $i] :
( ~ ( b @ ( c @ ( a @ subtract ) @ add ) @ ( A @ equalish ) )
| ~ ( A @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( c @ ( b @ subtract ) @ ( a @ add ) )),bind(B,$thf( B )),bind(C,$thf( b @ ( c @ ( a @ subtract ) @ add ) ))]]) ).
thf(112,plain,
! [A: $i] :
( ~ ( b @ ( c @ ( a @ subtract ) @ add ) @ ( A @ equalish ) )
| ~ ( A @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ subtract ) @ add ) @ ( C @ ( B @ ( A @ add ) @ subtract ) @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( D @ equalish ) ) )
| ~ $true
| ~ ( D @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[24,112]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ subtract ) @ add ) @ ( C @ ( B @ ( A @ add ) @ subtract ) @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( D @ equalish ) ) )
| ~ ( D @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
~ ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( c )),bind(D,$thf( c @ ( b @ ( a @ add ) @ subtract ) ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(19,plain,
! [B: $i,A: $i] : ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,15]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ add ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) )
| ( ( B @ ( A @ add ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ add ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) )
| ( B
!= ( c @ ( b @ subtract ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[40]) ).
thf(60,plain,
( ( a @ ( c @ ( b @ subtract ) @ add ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ ( a @ subtract ) @ add ) )
!= ( B @ ( A @ add ) ) )
| ( ( A @ ( B @ add ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) )
| ( ( B @ ( A @ add ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[40]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( b @ ( c @ ( a @ subtract ) @ add ) )
!= ( B @ ( A @ add ) ) )
| ( A
!= ( c @ ( b @ subtract ) ) )
| ( B != a )
| ( B
!= ( c @ ( b @ subtract ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[45]) ).
thf(65,plain,
( ( ( b @ ( c @ ( a @ subtract ) @ add ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) )
| ( ( c @ ( b @ subtract ) )
!= a ) ),
inference(simp,[status(thm)],[48]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( C @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ ( b @ ( c @ ( a @ subtract ) @ add ) @ ( C @ equalish ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,112]) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( C @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ ( b @ ( c @ ( a @ subtract ) @ add ) @ ( C @ equalish ) ) ),
inference(simp,[status(thm)],[254]) ).
thf(256,plain,
~ ( b @ ( c @ ( a @ subtract ) @ add ) @ ( a @ ( c @ ( b @ subtract ) @ add ) @ equalish ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( a )),bind(B,$thf( c @ ( b @ subtract ) )),bind(C,$thf( a @ ( c @ ( b @ subtract ) @ add ) ))]]) ).
thf(7,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_inverts_subtraction2) ).
thf(22,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,15]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ add ) @ subtract ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) )
| ( A
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
! [A: $i] :
( ( A @ ( A @ ( c @ ( b @ subtract ) @ ( a @ add ) @ add ) @ subtract ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(16,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(293,plain,
! [A: $i] :
( ( ( A @ ( A @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,249]) ).
thf(294,plain,
! [A: $i] :
( ( A @ ( A @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(308,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ ( a @ add ) @ subtract ) ) )
| ( A
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(313,plain,
( ( c @ ( b @ ( a @ add ) @ subtract ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ),
inference(simp,[status(thm)],[308]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( A != b )
| ( B
!= ( c @ ( a @ subtract ) ) )
| ( B
!= ( c @ ( b @ subtract ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[40]) ).
thf(62,plain,
( ( b != a )
| ( ( c @ ( b @ subtract ) )
!= ( c @ ( a @ subtract ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(80,plain,
( ( b != a )
| ( c != c )
| ( b != a ) ),
inference(simp,[status(thm)],[62]) ).
thf(81,plain,
b != a,
inference(simp,[status(thm)],[80]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_inverts_subtraction1) ).
thf(21,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,15]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( A
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) )
| ( ( B @ ( B @ ( A @ add ) @ subtract ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
! [A: $i] :
( ( A @ ( A @ ( b @ ( c @ ( a @ subtract ) @ add ) @ add ) @ subtract ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(82,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) )
!= ( D @ ( C @ equalish ) ) )
| ( E @ ( C @ equalish ) )
| ~ ( E @ ( D @ equalish ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,18]) ).
thf(83,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) )
!= ( D @ ( C @ equalish ) ) )
| ( E @ ( C @ equalish ) )
| ~ ( E @ ( D @ equalish ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( C @ add ) @ subtract ) @ equalish ) )
| ~ ( A @ ( C @ equalish ) ) ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( H @ add ) @ subtract ) )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( C @ add ) @ subtract ) @ equalish ) )
| ~ ( A @ ( C @ equalish ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(33,plain,
! [A: $i] :
( ( ( A @ ( A @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,15]) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( A @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
! [A: $i] :
( ( A
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) )
| ( A
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
( ( c @ ( b @ subtract ) @ ( a @ add ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
( ( ( c @ ( b @ subtract ) )
!= b )
| ( ( c @ ( a @ subtract ) )
!= a ) ),
inference(simp,[status(thm)],[36]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ add ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution1) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ add ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ subtract ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ subtract ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_substitution1) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ subtract ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ subtract ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A != b )
| ( B
!= ( c @ ( a @ subtract ) ) )
| ( ( B @ ( A @ add ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(61,plain,
( ( c @ ( a @ subtract ) @ ( b @ add ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[18,249]) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[290]) ).
thf(292,plain,
! [A: $i] :
( ~ ( c @ ( b @ ( a @ add ) @ subtract ) @ ( A @ equalish ) )
| ~ ( A @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( c @ ( b @ subtract ) @ ( a @ add ) )),bind(B,$thf( B )),bind(C,$thf( c @ ( b @ ( a @ add ) @ subtract ) ))]]) ).
thf(312,plain,
! [A: $i] :
( ~ ( c @ ( b @ ( a @ add ) @ subtract ) @ ( A @ equalish ) )
| ~ ( A @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[292]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution2) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(198,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( C @ ( E @ equalish ) ) )
| ( C @ ( D @ ( D @ ( E @ add ) @ subtract ) @ equalish ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,111]) ).
thf(199,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( C @ ( E @ equalish ) ) )
| ( C @ ( D @ ( D @ ( E @ add ) @ subtract ) @ equalish ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ add ) @ ( A @ ( A @ ( B @ ( C @ add ) @ add ) @ subtract ) @ equalish ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ add ) )),bind(D,$thf( D )),bind(E,$thf( H @ ( I @ add ) ))]]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ add ) @ ( A @ ( A @ ( B @ ( C @ add ) @ add ) @ subtract ) @ equalish ) ),
inference(simp,[status(thm)],[200]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,249]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( b @ ( a @ add ) @ subtract ) ) )
| ( ( B @ ( B @ ( A @ add ) @ subtract ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(311,plain,
! [A: $i] :
( ( A @ ( A @ ( c @ ( b @ ( a @ add ) @ subtract ) @ add ) @ subtract ) )
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(584,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( C @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ ( c @ ( b @ ( a @ add ) @ subtract ) @ ( C @ equalish ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,312]) ).
thf(585,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( C @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ ( c @ ( b @ ( a @ add ) @ subtract ) @ ( C @ equalish ) ) ),
inference(simp,[status(thm)],[584]) ).
thf(586,plain,
~ ( c @ ( b @ ( a @ add ) @ subtract ) @ ( a @ ( c @ ( b @ subtract ) @ add ) @ equalish ) ),
inference(pattern_uni,[status(thm)],[585:[bind(A,$thf( a )),bind(B,$thf( c @ ( b @ subtract ) )),bind(C,$thf( a @ ( c @ ( b @ subtract ) @ add ) ))]]) ).
thf(629,plain,
! [A: $i] :
( ( ( A @ ( A @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( a @ ( c @ ( b @ subtract ) @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,586]) ).
thf(630,plain,
! [A: $i] :
( ( A @ ( A @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( a @ ( c @ ( b @ subtract ) @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[629]) ).
thf(648,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ ( a @ add ) @ subtract ) ) )
| ( A
!= ( a @ ( c @ ( b @ subtract ) @ add ) ) ) ),
inference(simp,[status(thm)],[630]) ).
thf(657,plain,
( ( c @ ( b @ ( a @ add ) @ subtract ) )
!= ( a @ ( c @ ( b @ subtract ) @ add ) ) ),
inference(simp,[status(thm)],[648]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( C @ equalish ) ) )
| ~ $true
| ~ ( C @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[19,112]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( C @ equalish ) ) )
| ~ ( C @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
~ ( c @ ( a @ subtract ) @ ( b @ add ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( b )),bind(B,$thf( c @ ( a @ subtract ) )),bind(C,$thf( c @ ( a @ subtract ) @ ( b @ add ) ))]]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( a @ ( c @ ( b @ subtract ) @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,256]) ).
thf(430,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) @ ( a @ ( c @ ( b @ subtract ) @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[429]) ).
thf(453,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ add ) @ subtract ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) )
| ( A
!= ( a @ ( c @ ( b @ subtract ) @ add ) ) ) ),
inference(simp,[status(thm)],[430]) ).
thf(458,plain,
! [A: $i] :
( ( A @ ( A @ ( a @ ( c @ ( b @ subtract ) @ add ) @ add ) @ subtract ) )
!= ( b @ ( c @ ( a @ subtract ) @ add ) ) ),
inference(simp,[status(thm)],[453]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ subtract ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ subtract ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_substitution2) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ subtract ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ subtract ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,249]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) @ ( c @ ( b @ subtract ) @ ( a @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ add ) @ subtract ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) ) )
| ( A
!= ( c @ ( b @ subtract ) @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[289]) ).
thf(315,plain,
! [A: $i] :
( ( A @ ( A @ ( c @ ( b @ subtract ) @ ( a @ add ) @ add ) @ subtract ) )
!= ( c @ ( b @ ( a @ add ) @ subtract ) ) ),
inference(simp,[status(thm)],[303]) ).
thf(812,plain,
! [A: $i] :
( ( A != c )
| ( ( A @ ( c @ ( b @ subtract ) @ ( a @ add ) @ add ) )
!= ( b @ ( a @ add ) ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(813,plain,
( ( c @ ( c @ ( b @ subtract ) @ ( a @ add ) @ add ) )
!= ( b @ ( a @ add ) ) ),
inference(simp,[status(thm)],[812]) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ add ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ add ) @ subtract ) @ ( C @ ( B @ ( A @ subtract ) @ add ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity1) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ add ) @ subtract ) @ ( C @ ( B @ ( A @ subtract ) @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(902,plain,
$false,
inference(e,[status(thm)],[249,14,60,65,256,129,17,313,81,18,79,15,111,24,37,25,20,29,61,312,28,21,205,311,657,586,22,259,27,112,458,16,31,813,40,26,23,315,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.61 % Computer : n011.cluster.edu
% 0.13/0.61 % Model : x86_64 x86_64
% 0.13/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.61 % Memory : 8046.5625MB
% 0.13/0.61 % OS : Linux 6.8.0-71-generic
% 0.13/0.61 % CPULimit : 300
% 0.13/0.61 % WCLimit : 300
% 0.13/0.61 % DateTime : Sat Sep 26 01:52:00 UTC 2026
% 0.13/0.61 % CPUTime :
% 0.13/0.61 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.92/1.34 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.59 % [INFO] Parsing done (245ms).
% 1.38/1.61 % [INFO] Running in sequential loop mode.
% 1.76/2.01 % [INFO] eprover registered as external prover.
% 1.76/2.01 % [INFO] Scanning for conjecture ...
% 1.98/2.14 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.13/2.19 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.21/2.23 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/2.23 % [INFO] Type checking passed.
% 2.21/2.24 % [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 ...
% 9.39/5.29 % External prover 'e' found a proof!
% 9.39/5.29 % [INFO] Killing All external provers ...
% 9.39/5.29 % Time passed: 4491ms (effective reasoning time: 3669ms)
% 9.39/5.29 % Axioms used in derivation (12): addition_inverts_subtraction1, addition_inverts_subtraction2, subtract_substitution1, reflexivity, transitivity, add_substitution2, commutativity1, associativity_of_addition, commutativity_of_addition, commutativity2, add_substitution1, subtract_substitution2
% 9.39/5.29 % No. of inferences in proof: 108
% 9.39/5.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4491 ms resp. 3669 ms w/o parsing
% 8.59/5.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.59/5.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------