%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP776+1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n019.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 07:21:57 AM UTC 2026
% Result : Theorem 63.05s 13.98s
% Output : Refutation 63.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 122 ( 29 unt; 0 typ; 1 def)
% Number of atoms : 296 ( 187 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1330 ( 138 ~; 114 |; 17 &;1031 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 253 ( 0 ^; 252 !; 0 ?; 253 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i ).
thf(eh_decl,type,
eh: $i ).
thf(eg_decl,type,
eg: $i ).
thf(g_decl,type,
g: $i > $o ).
thf(inv_decl,type,
inv: $i > $i ).
thf(opp_decl,type,
opp: $i > $i ).
thf(h_decl,type,
h: $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(product_decl,type,
product: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ inv @ f )
= ( A @ f @ opp ) )
| ~ ( A @ g ) ) ) ) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ product ) @ f )
= ( A @ f @ ( B @ f @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos18) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ product ) @ f )
= ( A @ f @ ( B @ f @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ product ) @ f )
= ( A @ f @ ( B @ f @ sum ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ product ) @ f )
= ( A @ f @ ( B @ f @ sum ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( ( A @ inv @ f )
= ( A @ f @ opp ) )
| ~ ( A @ g ) )
& ( ( eh @ f )
= eg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( ( A @ inv @ f )
= ( A @ f @ opp ) )
| ~ ( A @ g ) )
& ( ( eh @ f )
= eg ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ( ( ( A @ inv @ f )
= ( A @ f @ opp ) )
| ~ ( A @ g ) )
& ( ( eh @ f )
= eg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ( ! [A: $i] :
( ( ( A @ inv @ f )
= ( A @ f @ opp ) )
| ~ ( A @ g ) )
& ( ( eh @ f )
= eg ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
( ( ( ( sk1 @ inv @ f )
!= ( sk1 @ f @ opp ) )
| ( ( eh @ f )
!= eg ) )
& ( ( sk1 @ g )
| ( ( eh @ f )
!= eg ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(25,plain,
( ( ( sk1 @ inv @ f )
!= ( sk1 @ f @ opp ) )
| ( ( eh @ f )
!= eg ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(27,plain,
( ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( eh @ f )
!= eg ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f )
!= ( eh @ f ) )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( A @ f @ ( B @ f @ sum ) )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[35,27]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( A @ f @ ( B @ f @ sum ) )
!= eg ) ),
inference(simp,[status(thm)],[120]) ).
thf(137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( B @ f @ sum ) )
!= ( C @ f @ ( D @ f @ sum ) ) )
| ( ( C @ ( D @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( A @ ( B @ product ) @ f )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[35,124]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( A @ ( B @ product ) @ f )
!= eg ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ g )
=> ( ( A @ ( A @ inv @ product ) )
= eh ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
thf(42,plain,
! [A: $i] :
( ( A @ g )
=> ( ( A @ ( A @ inv @ product ) )
= eh ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
eh @ g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
thf(67,plain,
eh @ g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ g )
=> ( ( A @ ( eh @ product ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
thf(36,plain,
! [A: $i] :
( ( A @ g )
=> ( ( A @ ( eh @ product ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,plain,
! [A: $i] :
( ( ( A @ ( eh @ product ) )
= A )
| ~ ( A @ g ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [A: $i] :
( ~ ( A @ g )
| ( ( A @ ( eh @ product ) )
= A ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(2120,plain,
! [A: $i] :
( ( ( eh @ g )
!= ( A @ g ) )
| ~ $true
| ( ( A @ ( eh @ product ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[67,38]) ).
thf(2121,plain,
! [A: $i] :
( ( ( eh @ g )
!= ( A @ g ) )
| ( ( A @ ( eh @ product ) )
= A ) ),
inference(simp,[status(thm)],[2120]) ).
thf(2122,plain,
( ( eh @ ( eh @ product ) )
= eh ),
inference(pattern_uni,[status(thm)],[2121:[bind(A,$thf( eh ))]]) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f )
!= ( C @ f ) )
| ( ( A @ f @ ( B @ f @ sum ) @ ( D @ f @ sum ) )
= ( C @ ( D @ product ) @ f ) ) ),
inference(paramod_ordered,[status(thm)],[35,35]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( B @ f @ sum ) @ ( A @ f @ sum ) )
= ( C @ ( B @ product ) @ ( A @ product ) @ f ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ product ) ))]]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( B @ f @ sum ) @ ( A @ f @ sum ) )
= ( C @ ( B @ product ) @ ( A @ product ) @ f ) ),
inference(simp,[status(thm)],[75]) ).
thf(95,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( B @ f @ sum ) )
!= ( E @ f @ ( D @ f @ sum ) ) )
| ( ( A @ ( B @ product ) @ f @ ( C @ f @ sum ) )
= ( E @ ( D @ product ) @ ( C @ product ) @ f ) ) ),
inference(paramod_ordered,[status(thm)],[35,78]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ product ) @ f @ ( C @ f @ sum ) )
= ( A @ ( B @ product ) @ ( C @ product ) @ f ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f @ ( C @ f @ sum ) )
!= ( D @ f @ ( E @ f @ sum ) ) )
| ( ( D @ ( E @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( A @ ( B @ product ) @ ( C @ product ) @ f )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[96,124]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ product ) @ ( A @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( C @ ( B @ product ) @ ( A @ product ) @ f )
!= eg ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G @ ( F @ product ) )),bind(E,$thf( C ))]]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ product ) @ ( A @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( C @ ( B @ product ) @ ( A @ product ) @ f )
!= eg ) ),
inference(simp,[status(thm)],[183]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ h )
=> ( ( eg @ ( A @ sum ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
thf(60,plain,
! [A: $i] :
( ( A @ h )
=> ( ( eg @ ( A @ sum ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,plain,
( ( sk1 @ g )
| ( ( eh @ f )
!= eg ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(26,plain,
( ( sk1 @ g )
| ( ( eh @ f )
!= eg ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f )
!= ( eh @ f ) )
| ( sk1 @ g )
| ( ( A @ f @ ( B @ f @ sum ) )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[35,26]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) )
!= eh )
| ( ( A @ f @ ( B @ f @ sum ) )
!= eg )
| ( sk1 @ g ) ),
inference(simp,[status(thm)],[214]) ).
thf(228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( B @ f @ sum ) )
!= ( C @ f @ ( D @ f @ sum ) ) )
| ( ( C @ ( D @ product ) )
!= eh )
| ( ( A @ ( B @ product ) @ f )
!= eg )
| ( sk1 @ g ) ),
inference(paramod_ordered,[status(thm)],[35,217]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) )
!= eh )
| ( ( A @ ( B @ product ) @ f )
!= eg )
| ( sk1 @ g ) ),
inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(155,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ ( C @ product ) @ f )
!= ( F @ ( E @ product ) @ ( D @ product ) @ f ) )
| ( ( A @ ( B @ product ) @ f @ ( C @ f @ sum ) )
= ( F @ f @ ( E @ f @ sum ) @ ( D @ f @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[96,78]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ product ) @ f @ ( C @ f @ sum ) )
= ( A @ f @ ( B @ f @ sum ) @ ( C @ f @ sum ) ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ h )
=> ( ( A @ ( eg @ sum ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
thf(71,plain,
! [A: $i] :
( ( A @ h )
=> ( ( A @ ( eg @ sum ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ g )
& ( B @ g )
& ( C @ g ) )
=> ( ( A @ ( B @ ( C @ product ) @ product ) )
= ( A @ ( B @ product ) @ ( C @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ g )
& ( B @ g )
& ( C @ g ) )
=> ( ( A @ ( B @ ( C @ product ) @ product ) )
= ( A @ ( B @ product ) @ ( C @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ g )
=> ( A @ inv @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
thf(58,plain,
! [A: $i] :
( ( A @ g )
=> ( A @ inv @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ h )
=> ( A @ opp @ h ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( B @ h )
=> ( A @ opp @ h ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(81,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ product ) @ ( A @ product ) @ f )
!= ( D @ ( E @ product ) @ f ) )
| ( ( C @ f @ ( B @ f @ sum ) @ ( A @ f @ sum ) )
= ( D @ f @ ( E @ f @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,35]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( B @ f @ sum ) @ ( A @ f @ sum ) )
= ( C @ ( B @ product ) @ f @ ( A @ f @ sum ) ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ product ) )),bind(E,$thf( A ))]]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( B @ f @ sum ) @ ( A @ f @ sum ) )
= ( C @ ( B @ product ) @ f @ ( A @ f @ sum ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(174,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f )
!= ( C @ ( D @ product ) @ f ) )
| ( ( A @ f @ ( B @ f @ sum ) @ ( E @ f @ sum ) )
= ( C @ ( D @ product ) @ ( E @ product ) @ f ) ) ),
inference(paramod_ordered,[status(thm)],[35,96]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ f @ ( B @ f @ sum ) @ ( C @ f @ sum ) )
= ( A @ ( B @ product ) @ ( C @ product ) @ f ) ),
inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ f @ ( B @ f @ sum ) @ ( C @ f @ sum ) )
= ( A @ ( B @ product ) @ ( C @ product ) @ f ) ),
inference(simp,[status(thm)],[175]) ).
thf(1067,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ f @ ( B @ f @ sum ) @ ( A @ f @ sum ) )
!= ( D @ f @ ( E @ f @ sum ) @ ( F @ f @ sum ) ) )
| ( ( C @ ( B @ product ) @ f @ ( A @ f @ sum ) )
= ( D @ ( E @ product ) @ ( F @ product ) @ f ) ) ),
inference(paramod_ordered,[status(thm)],[111,202]) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ f @ ( A @ f @ sum ) )
= ( C @ ( B @ product ) @ ( A @ product ) @ f ) ),
inference(pattern_uni,[status(thm)],[1067:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ h )
=> ( ( A @ opp @ ( A @ sum ) )
= eg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos15) ).
thf(52,plain,
! [A: $i] :
( ( A @ h )
=> ( ( A @ opp @ ( A @ sum ) )
= eg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f )
!= ( D @ f ) )
| ( ( C @ f @ ( A @ f @ ( B @ f @ sum ) @ sum ) )
= ( C @ ( D @ product ) @ f ) ) ),
inference(paramod_ordered,[status(thm)],[35,35]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ f @ ( C @ f @ ( B @ f @ sum ) @ sum ) )
= ( A @ ( C @ ( B @ product ) @ product ) @ f ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ product ) ))]]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ f @ ( C @ f @ ( B @ f @ sum ) @ sum ) )
= ( A @ ( C @ ( B @ product ) @ product ) @ f ) ),
inference(simp,[status(thm)],[77]) ).
thf(290,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( B @ f @ sum ) )
!= ( E @ f @ ( D @ f @ sum ) ) )
| ( ( C @ f @ ( A @ ( B @ product ) @ f @ sum ) )
= ( C @ ( E @ ( D @ product ) @ product ) @ f ) ) ),
inference(paramod_ordered,[status(thm)],[35,79]) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( A @ ( B @ product ) @ f @ sum ) )
= ( C @ ( A @ ( B @ product ) @ product ) @ f ) ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f )
!= ( C @ ( D @ product ) @ f ) )
| ( ( E @ f @ ( A @ f @ ( B @ f @ sum ) @ sum ) )
= ( E @ ( C @ ( D @ product ) @ product ) @ f ) ) ),
inference(paramod_ordered,[status(thm)],[35,291]) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( A @ f @ ( B @ f @ sum ) @ sum ) )
= ( C @ ( A @ ( B @ product ) @ product ) @ f ) ),
inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(504,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ f @ ( A @ f @ ( B @ f @ sum ) @ sum ) )
= ( C @ ( A @ ( B @ product ) @ product ) @ f ) ),
inference(simp,[status(thm)],[408]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f )
!= ( sk1 @ f ) )
| ( ( A @ f @ ( B @ f @ sum ) @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( eh @ f )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[35,27]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) )
!= sk1 )
| ( ( A @ f @ ( B @ f @ sum ) @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( eh @ f )
!= eg ) ),
inference(simp,[status(thm)],[121]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ h )
& ( B @ h ) )
=> ( A @ ( B @ sum ) @ h ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( ( A @ h )
& ( B @ h ) )
=> ( A @ ( B @ sum ) @ h ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sum ) @ h )
| ~ ( A @ h )
| ~ ( B @ h ) ),
inference(cnf,[status(esa)],[28]) ).
thf(2123,plain,
! [A: $i] :
( ( ( sk1 @ g )
!= ( A @ g ) )
| ~ $true
| ( ( A @ ( eh @ product ) )
= A )
| ( ( eh @ f )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[26,38]) ).
thf(2124,plain,
! [A: $i] :
( ( ( sk1 @ g )
!= ( A @ g ) )
| ( ( A @ ( eh @ product ) )
= A )
| ( ( eh @ f )
!= eg ) ),
inference(simp,[status(thm)],[2123]) ).
thf(2125,plain,
( ( ( sk1 @ ( eh @ product ) )
= sk1 )
| ( ( eh @ f )
!= eg ) ),
inference(pattern_uni,[status(thm)],[2124:[bind(A,$thf( sk1 ))]]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ product ) @ product ) )
= ( A @ ( B @ product ) @ ( C @ product ) ) )
| ~ ( A @ g )
| ~ ( B @ g )
| ~ ( C @ g ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ g )
| ~ ( B @ g )
| ~ ( C @ g )
| ( ( A @ ( B @ ( C @ product ) @ product ) )
= ( A @ ( B @ product ) @ ( C @ product ) ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(43,plain,
! [A: $i] :
( ( ( A @ ( A @ inv @ product ) )
= eh )
| ~ ( A @ g ) ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ~ ( A @ g )
| ( ( A @ ( A @ inv @ product ) )
= eh ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(3199,plain,
! [A: $i] :
( ( ( eh @ g )
!= ( A @ g ) )
| ~ $true
| ( ( A @ ( A @ inv @ product ) )
= eh ) ),
inference(paramod_ordered,[status(thm)],[67,44]) ).
thf(3200,plain,
! [A: $i] :
( ( ( eh @ g )
!= ( A @ g ) )
| ( ( A @ ( A @ inv @ product ) )
= eh ) ),
inference(simp,[status(thm)],[3199]) ).
thf(3201,plain,
( ( eh @ ( eh @ inv @ product ) )
= eh ),
inference(pattern_uni,[status(thm)],[3200:[bind(A,$thf( eh ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ h )
& ( B @ h )
& ( C @ h ) )
=> ( ( A @ ( B @ ( C @ sum ) @ sum ) )
= ( A @ ( B @ sum ) @ ( C @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ h )
& ( B @ h )
& ( C @ h ) )
=> ( ( A @ ( B @ ( C @ sum ) @ sum ) )
= ( A @ ( B @ sum ) @ ( C @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sum ) @ sum ) )
= ( A @ ( B @ sum ) @ ( C @ sum ) ) )
| ~ ( A @ h )
| ~ ( B @ h )
| ~ ( C @ h ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ h )
| ~ ( B @ h )
| ~ ( C @ h )
| ( ( A @ ( B @ ( C @ sum ) @ sum ) )
= ( A @ ( B @ sum ) @ ( C @ sum ) ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ g )
=> ( ( eh @ ( A @ product ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
thf(45,plain,
! [A: $i] :
( ( A @ g )
=> ( ( eh @ ( A @ product ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f @ ( B @ f @ sum ) )
!= ( C @ f @ ( D @ f @ sum ) ) )
| ( ( C @ ( D @ product ) )
!= sk1 )
| ( ( A @ ( B @ product ) @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( eh @ f )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[35,125]) ).
thf(958,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ product ) )
!= sk1 )
| ( ( A @ ( B @ product ) @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( eh @ f )
!= eg ) ),
inference(pattern_uni,[status(thm)],[957:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(454,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ f @ ( A @ ( B @ product ) @ f @ sum ) )
!= ( D @ f @ ( E @ f @ sum ) ) )
| ( ( D @ ( E @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( C @ ( A @ ( B @ product ) @ product ) @ f )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[291,124]) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ product ) @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( A @ ( C @ ( B @ product ) @ product ) @ f )
!= eg ) ),
inference(pattern_uni,[status(thm)],[454:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( G @ ( F @ product ) ))]]) ).
thf(494,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ product ) @ product ) )
!= eh )
| ( ( sk1 @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( A @ ( C @ ( B @ product ) @ product ) @ f )
!= eg ) ),
inference(simp,[status(thm)],[455]) ).
thf(17,axiom,
eg @ h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
thf(66,plain,
eg @ h,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2251,plain,
! [B: $i,A: $i] :
( ( ( eh @ ( eh @ product ) )
!= ( A @ ( B @ product ) ) )
| ( ( A @ f @ ( B @ f @ sum ) )
= ( eh @ f ) ) ),
inference(paramod_ordered,[status(thm)],[2122,35]) ).
thf(2252,plain,
( ( eh @ f @ ( eh @ f @ sum ) )
= ( eh @ f ) ),
inference(pattern_uni,[status(thm)],[2251:[bind(A,$thf( eh )),bind(B,$thf( eh ))]]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( A @ g )
& ( B @ g ) )
=> ( A @ ( B @ product ) @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( A @ g )
& ( B @ g ) )
=> ( A @ ( B @ product ) @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ g )
=> ( ( A @ inv @ ( A @ product ) )
= eh ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
thf(63,plain,
! [A: $i] :
( ( A @ g )
=> ( ( A @ inv @ ( A @ product ) )
= eh ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(2848,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( eh @ product ) )
!= ( A @ ( B @ product ) ) )
| ( sk1 != sk1 )
| ( ( A @ ( B @ product ) @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( eh @ f )
!= eg )
| ( ( eh @ f )
!= eg ) ),
inference(paramod_ordered,[status(thm)],[2125,958]) ).
thf(2849,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( eh @ product ) )
!= ( A @ ( B @ product ) ) )
| ( ( A @ ( B @ product ) @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( eh @ f )
!= eg ) ),
inference(simp,[status(thm)],[2848]) ).
thf(2850,plain,
( ( ( sk1 @ ( eh @ product ) @ f @ opp )
!= ( sk1 @ inv @ f ) )
| ( ( eh @ f )
!= eg ) ),
inference(pattern_uni,[status(thm)],[2849:[bind(A,$thf( sk1 )),bind(B,$thf( eh ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ g )
=> ( A @ f @ h ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos17) ).
thf(50,plain,
! [A: $i] :
( ( A @ g )
=> ( A @ f @ h ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ h )
=> ( ( A @ ( A @ opp @ sum ) )
= eg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
thf(55,plain,
! [A: $i] :
( ( A @ h )
=> ( ( A @ ( A @ opp @ sum ) )
= eg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(230,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ product ) @ f @ ( C @ f @ sum ) )
!= ( D @ f @ ( E @ f @ sum ) ) )
| ( ( D @ ( E @ product ) )
!= eh )
| ( ( A @ ( B @ product ) @ ( C @ product ) @ f )
!= eg )
| ( sk1 @ g ) ),
inference(paramod_ordered,[status(thm)],[96,217]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ product ) @ ( A @ product ) )
!= eh )
| ( ( C @ ( B @ product ) @ ( A @ product ) @ f )
!= eg )
| ( sk1 @ g ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G @ ( F @ product ) )),bind(E,$thf( C ))]]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ product ) @ ( A @ product ) )
!= eh )
| ( ( C @ ( B @ product ) @ ( A @ product ) @ f )
!= eg )
| ( sk1 @ g ) ),
inference(simp,[status(thm)],[231]) ).
thf(2256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( eh @ ( eh @ product ) )
!= ( C @ ( B @ product ) ) )
| ( ( eh @ f @ ( A @ f @ sum ) )
= ( C @ ( B @ product ) @ ( A @ product ) @ f ) ) ),
inference(paramod_ordered,[status(thm)],[2122,1068]) ).
thf(2257,plain,
! [A: $i] :
( ( eh @ f @ ( A @ f @ sum ) )
= ( eh @ ( eh @ product ) @ ( A @ product ) @ f ) ),
inference(pattern_uni,[status(thm)],[2256:[bind(A,$thf( A )),bind(B,$thf( eh )),bind(C,$thf( eh ))]]) ).
thf(2470,plain,
! [A: $i] :
( ( eh @ f @ ( A @ f @ sum ) )
= ( eh @ ( A @ product ) @ f ) ),
inference(rewrite,[status(thm)],[2257,2122]) ).
thf(393,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ f @ ( A @ ( B @ product ) @ f @ sum ) )
!= ( D @ f @ ( E @ f @ sum ) ) )
| ( ( D @ ( E @ product ) )
!= eh )
| ( ( C @ ( A @ ( B @ product ) @ product ) @ f )
!= eg )
| ( sk1 @ g ) ),
inference(paramod_ordered,[status(thm)],[291,217]) ).
thf(394,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ product ) @ product ) )
!= eh )
| ( ( A @ ( C @ ( B @ product ) @ product ) @ f )
!= eg )
| ( sk1 @ g ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( G @ ( F @ product ) ))]]) ).
thf(496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ product ) @ product ) )
!= eh )
| ( ( A @ ( C @ ( B @ product ) @ product ) @ f )
!= eg )
| ( sk1 @ g ) ),
inference(simp,[status(thm)],[394]) ).
thf(16047,plain,
$false,
inference(e,[status(thm)],[138,42,2122,206,60,229,156,71,39,35,58,68,217,1068,202,52,504,125,78,29,21,33,28,38,124,96,2125,41,3201,32,45,44,291,958,27,494,66,2252,48,63,2850,50,67,26,55,36,30,239,79,111,2470,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP776+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.11 % 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
% 0.23/0.49 % Computer : n019.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Fri Sep 25 15:46:19 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.50 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
% 1.34/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.86/1.60 % [INFO] Parsing done (269ms).
% 1.86/1.62 % [INFO] Running in sequential loop mode.
% 2.84/2.23 % [INFO] eprover registered as external prover.
% 2.84/2.24 % [INFO] Scanning for conjecture ...
% 3.01/2.37 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.17/2.47 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.35/2.52 % [INFO] Problem is first-order (TPTP FOF).
% 3.35/2.53 % [INFO] Type checking passed.
% 3.35/2.54 % [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 ...
% 63.05/13.98 % External prover 'e' found a proof!
% 63.05/13.98 % [INFO] Killing All external provers ...
% 63.05/13.98 % Time passed: 13275ms (effective reasoning time: 12344ms)
% 63.05/13.98 % Solved by 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)>
% 63.05/13.98 % Axioms used in derivation (18): sos14, sos06, sos13, sos10, sos09, sos02, sos11, sos08, sos12, sos04, sos15, sos17, sos03, sos16, sos05, sos07, sos01, sos18
% 63.05/13.98 % No. of inferences in proof: 121
% 63.05/13.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13275 ms resp. 12344 ms w/o parsing
% 63.97/14.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 63.97/14.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------