%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n001.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 06:50:19 AM UTC 2026
% Result : Unsatisfiable 9.61s 3.18s
% Output : Refutation 8.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 109 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 275 ( 83 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1165 ( 124 ~; 110 |; 0 &; 931 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 213 ( 0 ^; 213 !; 0 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(c_Orderings_Omax_decl,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(v_g_decl,type,
v_g: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(v_h_decl,type,
v_h: $i > $i ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(1,negated_conjecture,
! [A: $i] : ( t_b @ ( t_b @ ( t_b @ ( A @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( t_b @ ( c_0 @ ( t_b @ ( A @ v_g @ ( A @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(17,plain,
! [A: $i] : ( t_b @ ( t_b @ ( t_b @ ( A @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( t_b @ ( c_0 @ ( t_b @ ( A @ v_g @ ( A @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(19,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(47,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(48,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[47]) ).
thf(79,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_Orderings_Olinorder )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,48]) ).
thf(80,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[79]) ).
thf(81,plain,
t_b @ class_Orderings_Olinorder,
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( t_b ))]]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Orderings_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Ole__maxI2_0) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Orderings_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Orderings_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[41]) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ( A @ ( A @ ( B @ ( C @ c_Orderings_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,42]) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ( A @ ( A @ ( B @ ( C @ c_Orderings_Omax ) ) @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[428]) ).
thf(430,plain,
! [B: $i,A: $i] : ( t_b @ ( t_b @ ( A @ ( B @ c_Orderings_Omax ) ) @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( t_b ))]]) ).
thf(447,plain,
! [B: $i,A: $i] : ( t_b @ ( t_b @ ( A @ ( B @ c_Orderings_Omax ) ) @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[430]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(51,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(52,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[51]) ).
thf(131,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,52]) ).
thf(132,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
t_b @ class_OrderedGroup_Olordered__ab__group__abs,
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( t_b ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ( ( A @ ( B @ c_HOL_Oabs ) )
= B ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ $true
| ( ( A @ ( B @ c_HOL_Oabs ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[133,23]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ( ( A @ ( B @ c_HOL_Oabs ) )
= B ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ ( c_0 @ c_lessequals ) ) )
| ( ( t_b @ ( A @ c_HOL_Oabs ) )
= A ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( t_b ))]]) ).
thf(208,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ ( c_0 @ c_lessequals ) ) )
| ( ( t_b @ ( A @ c_HOL_Oabs ) )
= A ) ),
inference(simp,[status(thm)],[207]) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ ( B @ c_Orderings_Omax ) ) @ ( A @ c_lessequals ) ) )
!= ( t_b @ ( C @ ( c_0 @ c_lessequals ) ) ) )
| ~ $true
| ( ( t_b @ ( C @ c_HOL_Oabs ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[447,208]) ).
thf(454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ ( B @ c_Orderings_Omax ) ) @ ( A @ c_lessequals ) ) )
!= ( t_b @ ( C @ ( c_0 @ c_lessequals ) ) ) )
| ( ( t_b @ ( C @ c_HOL_Oabs ) )
= C ) ),
inference(simp,[status(thm)],[453]) ).
thf(455,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_HOL_Oabs ) )
= ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) ) ),
inference(pattern_uni,[status(thm)],[454:[bind(A,$thf( c_0 )),bind(B,$thf( D )),bind(C,$thf( t_b @ ( c_0 @ ( D @ c_Orderings_Omax ) ) ))]]) ).
thf(464,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) @ c_HOL_Oabs ) )
= ( t_b @ ( c_0 @ ( A @ c_Orderings_Omax ) ) ) ),
inference(simp,[status(thm)],[455]) ).
thf(468,plain,
! [A: $i] : ( t_b @ ( t_b @ ( t_b @ ( A @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( c_0 @ ( t_b @ ( A @ v_g @ ( A @ v_f @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[17,464]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(49,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[49]) ).
thf(107,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,50]) ).
thf(108,plain,
! [A: $i] :
( ( ( t_b @ class_Ring__and__Field_Oordered__idom )
!= ( A @ class_Ring__and__Field_Oordered__idom ) )
| ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
t_b @ class_OrderedGroup_Oab__group__add,
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( t_b ))]]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_plus ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_plus ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_plus ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_plus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_plus ) ) @ c_uminus ) ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_plus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_plus ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,34]) ).
thf(528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_plus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_plus ) ) @ c_uminus ) ) ) ),
inference(simp,[status(thm)],[527]) ).
thf(529,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( t_b @ ( A @ c_uminus ) @ c_plus ) ) )
= ( t_b @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[528:[bind(A,$thf( t_b ))]]) ).
thf(567,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( t_b @ ( A @ c_uminus ) @ c_plus ) ) )
= ( t_b @ ( t_b @ ( B @ ( A @ c_plus ) ) @ c_uminus ) ) ),
inference(simp,[status(thm)],[529]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[109,40]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( t_b ))]]) ).
thf(296,plain,
! [A: $i] :
( ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(simp,[status(thm)],[288]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__1_0) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,26]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ class_OrderedGroup_Oab__group__add )
!= ( A @ class_OrderedGroup_Oab__group__add ) )
| ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_minus ) ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_plus ) ) )
= ( t_b @ ( B @ ( A @ c_minus ) ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( t_b ))]]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_plus ) ) )
= ( t_b @ ( B @ ( A @ c_minus ) ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ c_uminus ) @ c_uminus ) )
!= ( t_b @ ( C @ c_uminus ) ) )
| ( ( t_b @ ( A @ ( B @ c_plus ) ) )
= ( t_b @ ( C @ ( B @ c_minus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[296,117]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( A @ c_plus ) ) )
= ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_minus ) ) ) ),
inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( t_b @ ( D @ c_uminus ) ))]]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( t_b @ ( B @ ( A @ c_plus ) ) )
= ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_minus ) ) ) ),
inference(simp,[status(thm)],[301]) ).
thf(574,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( B @ c_uminus ) @ c_uminus ) @ ( t_b @ ( A @ c_uminus ) @ c_minus ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( B @ c_uminus ) @ ( A @ c_minus ) ) @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[567,315]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_0) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(cnf,[status(esa)],[27]) ).
thf(2,negated_conjecture,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( A @ v_x @ v_g @ c_plus ) ) @ ( A @ v_x @ v_f @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(18,plain,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( A @ v_x @ v_g @ c_plus ) ) @ ( A @ v_x @ v_f @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( A @ v_x @ v_g @ c_plus ) ) @ ( A @ v_x @ v_f @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(250,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( B @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( E @ v_x @ v_h @ c_HOL_Oabs ) @ ( E @ c_times ) ) @ ( E @ v_x @ v_g @ c_plus ) ) @ ( E @ v_x @ v_f @ c_lessequals ) ) ) )
| ~ $true
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(paramod_ordered,[status(thm)],[28,20]) ).
thf(251,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( B @ c_lessequals ) ) )
!= ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( E @ v_x @ v_h @ c_HOL_Oabs ) @ ( E @ c_times ) ) @ ( E @ v_x @ v_g @ c_plus ) ) @ ( E @ v_x @ v_f @ c_lessequals ) ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(simp,[status(thm)],[250]) ).
thf(252,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ v_x @ v_g @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( A @ v_x @ v_f @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( t_b @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( t_b )),bind(B,$thf( P @ v_x @ v_f )),bind(C,$thf( t_b @ ( t_b @ ( P @ v_x @ v_h @ c_HOL_Oabs ) @ ( P @ c_times ) ) )),bind(D,$thf( P @ v_x @ v_g )),bind(E,$thf( P ))]]) ).
thf(274,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ v_x @ v_g @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( A @ v_x @ v_f @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( t_b @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(simp,[status(thm)],[252]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(45,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[45]) ).
thf(202,plain,
! [A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[133,46]) ).
thf(203,plain,
! [A: $i] :
( ( ( t_b @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( A @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(simp,[status(thm)],[202]) ).
thf(204,plain,
t_b @ class_OrderedGroup_Opordered__ab__group__add,
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( t_b ))]]) ).
thf(329,plain,
! [A: $i] :
( ~ ( t_b @ ( A @ v_x @ v_g @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( A @ v_x @ v_f @ c_minus ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[274,204]) ).
thf(330,plain,
! [A: $i] :
~ ( t_b @ ( A @ v_x @ v_g @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( A @ v_x @ v_f @ c_minus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_minus ) ) @ c_uminus ) )
= ( A @ ( B @ ( C @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_minus ) ) @ c_uminus ) )
= ( A @ ( B @ ( C @ c_minus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( B @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( B @ class_OrderedGroup_Opordered__ab__group__add )
| ~ $true
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(paramod_ordered,[status(thm)],[52,46]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
!= ( B @ class_OrderedGroup_Olordered__ab__group__abs ) )
| ( B @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(simp,[status(thm)],[134]) ).
thf(136,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_minus ) ) )
= ( A @ ( C @ ( B @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_minus ) ) )
= ( A @ ( C @ ( B @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ class_OrderedGroup_Oab__group__add )
!= ( B @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( ( B @ ( B @ ( C @ c_uminus ) @ c_uminus ) )
= C )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(paramod_ordered,[status(thm)],[50,40]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ class_OrderedGroup_Oab__group__add )
!= ( B @ class_OrderedGroup_Oab__group__add ) )
| ( ( B @ ( B @ ( C @ c_uminus ) @ c_uminus ) )
= C )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(simp,[status(thm)],[289]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(simp,[status(thm)],[291]) ).
thf(448,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_b @ ( t_b @ ( A @ ( B @ c_Orderings_Omax ) ) @ ( A @ c_lessequals ) ) )
!= ( t_b @ ( C @ v_x @ v_g @ ( t_b @ ( t_b @ ( t_b @ ( C @ v_x @ v_h @ c_HOL_Oabs ) @ ( C @ c_times ) ) @ ( C @ v_x @ v_f @ c_minus ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[447,330]) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b @ ( t_b @ ( A @ ( B @ c_Orderings_Omax ) ) @ ( A @ c_lessequals ) ) )
!= ( t_b @ ( C @ v_x @ v_g @ ( t_b @ ( t_b @ ( t_b @ ( C @ v_x @ v_h @ c_HOL_Oabs ) @ ( C @ c_times ) ) @ ( C @ v_x @ v_f @ c_minus ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[448]) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ( t_b != t_b )
| ( ( t_b @ ( A @ ( B @ c_Orderings_Omax ) ) )
!= ( C @ v_x @ v_g ) )
| ( A
!= ( t_b @ ( t_b @ ( t_b @ ( C @ v_x @ v_h @ c_HOL_Oabs ) @ ( C @ c_times ) ) @ ( C @ v_x @ v_f @ c_minus ) ) ) ) ),
inference(simp,[status(thm)],[449]) ).
thf(466,plain,
! [B: $i,A: $i] :
( ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( B @ v_x @ v_h @ c_HOL_Oabs ) @ ( B @ c_times ) ) @ ( B @ v_x @ v_f @ c_minus ) ) @ ( A @ c_Orderings_Omax ) ) )
!= ( B @ v_x @ v_g ) ),
inference(simp,[status(thm)],[461]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_minus ) ) )
= ( A @ ( C @ ( B @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( ( A @ ( C @ ( B @ c_plus ) ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(319,plain,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ c_uminus ) @ ( A @ v_x @ v_g @ c_minus ) ) @ ( A @ v_x @ v_f @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[20,315]) ).
thf(747,plain,
$false,
inference(e,[status(thm)],[468,52,574,133,109,41,330,35,43,136,42,24,46,29,297,21,28,38,45,296,17,32,34,204,27,49,466,81,208,48,18,50,31,319,40,26,23,447,315,51,19,464,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.14/0.40 % Computer : n001.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 22:13:45 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.18 % [INFO] Parsing done (191ms).
% 1.36/1.20 % [INFO] Running in sequential loop mode.
% 1.76/1.56 % [INFO] eprover registered as external prover.
% 1.76/1.57 % [INFO] Scanning for conjecture ...
% 1.98/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 1.98/1.64 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.98/1.65 % [INFO] Problem is propositional (TPTP CNF).
% 1.98/1.66 % [INFO] Type checking passed.
% 1.98/1.66 % [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 ...
% 9.61/3.18 % External prover 'e' found a proof!
% 9.61/3.18 % [INFO] Killing All external provers ...
% 9.61/3.18 % Time passed: 2634ms (effective reasoning time: 1976ms)
% 9.61/3.18 % Axioms used in derivation (13): cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_OrderedGroup_Ocompare__rls__8_0, cls_OrderedGroup_Ominus__minus_0, cls_OrderedGroup_Ominus__add__distrib_0, cls_OrderedGroup_Ocompare__rls__1_0, clsrel_Ring__and__Field_Oordered__idom_4, cls_OrderedGroup_Oabs__of__nonneg_0, cls_Orderings_Ole__maxI2_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_OrderedGroup_Ominus__diff__eq_0, clsrel_OrderedGroup_Olordered__ab__group__abs_1, cls_OrderedGroup_Odiff__minus__eq__add_0, clsrel_Ring__and__Field_Oordered__idom_33
% 9.61/3.18 % No. of inferences in proof: 109
% 9.61/3.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2634 ms resp. 1976 ms w/o parsing
% 8.88/3.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.88/3.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------