%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRA117-1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n003.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 07:18:33 AM UTC 2026
% Result : Unsatisfiable 27.01s 6.29s
% Output : Refutation 23.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 121 ( 61 unt; 0 typ; 0 def)
% Number of atoms : 381 ( 161 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 773 ( 135 ~; 220 |; 0 &; 418 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 8 con; 0-2 aty)
% Number of variables : 88 ( 0 ^; 88 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(r_decl,type,
r: $i > $i > $o ).
thf(v0_decl,type,
v0: $i ).
thf(v1_decl,type,
v1: $i ).
thf(v2_decl,type,
v2: $i ).
thf(v3_decl,type,
v3: $i ).
thf(v4_decl,type,
v4: $i ).
thf(v5_decl,type,
v5: $i ).
thf(18,axiom,
v4 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4nv5) ).
thf(69,plain,
v4 != v5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ r ) )
| ( C @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( B = C )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rno3acl) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ r ) )
| ( C @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( B = C )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ r ) )
| ( C @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( B = C )
| ( A = C )
| ( A = B ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ r ) )
| ( C @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( B = C )
| ( A = C )
| ( A = B ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(9,axiom,
v2 != v3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2nv3) ).
thf(42,plain,
v2 != v3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,plain,
v2 != v3,
inference(polarity_switch,[status(thm)],[42]) ).
thf(44,plain,
v3 != v2,
inference(lifteq,[status(thm)],[43]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( C != v3 )
| ( B != v2 )
| ( C @ ( B @ r ) )
| ( C @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( A = C )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[26,44]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( B != v2 )
| ( v3 @ ( B @ r ) )
| ( v3 @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( A = v3 )
| ( A = B ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( v3 ))]]) ).
thf(157,plain,
! [A: $i] :
( ( v3 @ ( v2 @ r ) )
| ( v3 @ ( A @ r ) )
| ( v2 @ ( A @ r ) )
| ( A = v3 )
| ( A = v2 ) ),
inference(simp,[status(thm)],[131]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ( B != v3 )
| ( C != v2 )
| ( C @ ( B @ r ) )
| ( C @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( A = C )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[26,44]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( B != v2 )
| ( B @ ( v3 @ r ) )
| ( B @ ( A @ r ) )
| ( v3 @ ( A @ r ) )
| ( A = B )
| ( A = v3 ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( A )),bind(B,$thf( v3 ))]]) ).
thf(156,plain,
! [A: $i] :
( ( v2 @ ( v3 @ r ) )
| ( v2 @ ( A @ r ) )
| ( v3 @ ( A @ r ) )
| ( A = v2 )
| ( A = v3 ) ),
inference(simp,[status(thm)],[129]) ).
thf(13,axiom,
v3 != v4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3nv4) ).
thf(54,plain,
v3 != v4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(55,plain,
v3 != v4,
inference(polarity_switch,[status(thm)],[54]) ).
thf(56,plain,
v4 != v3,
inference(lifteq,[status(thm)],[55]) ).
thf(351,plain,
! [A: $i] :
( ( A != v4 )
| ( v3 != v3 )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( A @ r ) )
| ( v3 @ ( A @ r ) )
| ( A = v2 ) ),
inference(paramod_ordered,[status(thm)],[156,56]) ).
thf(352,plain,
! [A: $i] :
( ( A != v4 )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( A @ r ) )
| ( v3 @ ( A @ r ) )
| ( A = v2 ) ),
inference(simp,[status(thm)],[351]) ).
thf(353,plain,
( ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) )
| ( v3 @ ( v4 @ r ) )
| ( v4 = v2 ) ),
inference(pattern_uni,[status(thm)],[352:[bind(A,$thf( v4 ))]]) ).
thf(12,axiom,
v2 != v4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2nv4) ).
thf(51,plain,
v2 != v4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52,plain,
v2 != v4,
inference(polarity_switch,[status(thm)],[51]) ).
thf(53,plain,
v4 != v2,
inference(lifteq,[status(thm)],[52]) ).
thf(942,plain,
( ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) )
| ( v3 @ ( v4 @ r ) ) ),
inference(simplifyReflect,[status(thm)],[353,53]) ).
thf(1012,plain,
( ~ $true
| ( ( v3 @ ( v4 @ r ) )
!= ( v2 @ ( v4 @ r ) ) )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[942]) ).
thf(1016,plain,
( ( ( v3 @ ( v4 @ r ) )
!= ( v2 @ ( v4 @ r ) ) )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) ) ),
inference(simp,[status(thm)],[1012]) ).
thf(8,axiom,
v1 != v3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1nv3) ).
thf(39,plain,
v1 != v3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
v1 != v3,
inference(polarity_switch,[status(thm)],[39]) ).
thf(41,plain,
v3 != v1,
inference(lifteq,[status(thm)],[40]) ).
thf(17,axiom,
v3 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3nv5) ).
thf(66,plain,
v3 != v5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
v1 != v2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1nv2) ).
thf(33,plain,
v1 != v2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,plain,
v1 != v2,
inference(polarity_switch,[status(thm)],[33]) ).
thf(35,plain,
v2 != v1,
inference(lifteq,[status(thm)],[34]) ).
thf(1,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ r ) )
| ~ ( B @ ( A @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rsym) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ r ) )
| ~ ( B @ ( A @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ r ) )
| ~ ( B @ ( A @ r ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(943,plain,
! [B: $i,A: $i] :
( ( ( v3 @ ( v4 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ~ $true
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) ) ),
inference(paramod_ordered,[status(thm)],[942,20]) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( ( v3 @ ( v4 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) ) ),
inference(simp,[status(thm)],[943]) ).
thf(945,plain,
( ( v4 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) ) ),
inference(pattern_uni,[status(thm)],[944:[bind(A,$thf( v4 )),bind(B,$thf( v3 ))]]) ).
thf(1105,plain,
( ~ $true
| ( ( v2 @ ( v4 @ r ) )
!= ( v4 @ ( v3 @ r ) ) )
| ( v4 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[945]) ).
thf(1108,plain,
( ( ( v2 @ ( v4 @ r ) )
!= ( v4 @ ( v3 @ r ) ) )
| ( v4 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(simp,[status(thm)],[1105]) ).
thf(67,plain,
v3 != v5,
inference(polarity_switch,[status(thm)],[66]) ).
thf(68,plain,
v5 != v3,
inference(lifteq,[status(thm)],[67]) ).
thf(446,plain,
! [A: $i] :
( ( A != v5 )
| ( v3 != v3 )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( A @ r ) )
| ( v3 @ ( A @ r ) )
| ( A = v2 ) ),
inference(paramod_ordered,[status(thm)],[156,68]) ).
thf(447,plain,
! [A: $i] :
( ( A != v5 )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( A @ r ) )
| ( v3 @ ( A @ r ) )
| ( A = v2 ) ),
inference(simp,[status(thm)],[446]) ).
thf(448,plain,
( ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v5 @ r ) )
| ( v3 @ ( v5 @ r ) )
| ( v5 = v2 ) ),
inference(pattern_uni,[status(thm)],[447:[bind(A,$thf( v5 ))]]) ).
thf(16,axiom,
v2 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2nv5) ).
thf(63,plain,
v2 != v5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(64,plain,
v2 != v5,
inference(polarity_switch,[status(thm)],[63]) ).
thf(65,plain,
v5 != v2,
inference(lifteq,[status(thm)],[64]) ).
thf(2296,plain,
( ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v5 @ r ) )
| ( v3 @ ( v5 @ r ) ) ),
inference(simplifyReflect,[status(thm)],[448,65]) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ( ( v3 @ ( v5 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ~ $true
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v5 @ r ) ) ),
inference(paramod_ordered,[status(thm)],[2296,20]) ).
thf(2308,plain,
! [B: $i,A: $i] :
( ( ( v3 @ ( v5 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v5 @ r ) ) ),
inference(simp,[status(thm)],[2307]) ).
thf(2309,plain,
( ( v5 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v5 @ r ) ) ),
inference(pattern_uni,[status(thm)],[2308:[bind(A,$thf( v5 )),bind(B,$thf( v3 ))]]) ).
thf(2781,plain,
! [B: $i,A: $i] :
( ( ( v2 @ ( v5 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ~ $true
| ( v5 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(paramod_ordered,[status(thm)],[2309,20]) ).
thf(2782,plain,
! [B: $i,A: $i] :
( ( ( v2 @ ( v5 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ( v5 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(simp,[status(thm)],[2781]) ).
thf(2783,plain,
( ( v5 @ ( v2 @ r ) )
| ( v5 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(pattern_uni,[status(thm)],[2782:[bind(A,$thf( v5 )),bind(B,$thf( v2 ))]]) ).
thf(1013,plain,
( ~ $true
| ( ( v3 @ ( v4 @ r ) )
!= ( v2 @ ( v3 @ r ) ) )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[942]) ).
thf(1014,plain,
( ( ( v3 @ ( v4 @ r ) )
!= ( v2 @ ( v3 @ r ) ) )
| ( v2 @ ( v3 @ r ) )
| ( v2 @ ( v4 @ r ) ) ),
inference(simp,[status(thm)],[1013]) ).
thf(1039,plain,
! [B: $i,A: $i] :
( ( ( v2 @ ( v4 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ~ $true
| ( v4 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(paramod_ordered,[status(thm)],[945,20]) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ( ( v2 @ ( v4 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ( v4 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(simp,[status(thm)],[1039]) ).
thf(1041,plain,
( ( v4 @ ( v2 @ r ) )
| ( v4 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(pattern_uni,[status(thm)],[1040:[bind(A,$thf( v4 )),bind(B,$thf( v2 ))]]) ).
thf(14,axiom,
v0 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv5) ).
thf(57,plain,
v0 != v5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
v0 != v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv1) ).
thf(27,plain,
v0 != v1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
v0 != v1,
inference(polarity_switch,[status(thm)],[27]) ).
thf(29,plain,
v1 != v0,
inference(lifteq,[status(thm)],[28]) ).
thf(15,axiom,
v1 != v5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1nv5) ).
thf(60,plain,
v1 != v5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
v0 != v3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv3) ).
thf(36,plain,
v0 != v3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
v0 != v3,
inference(polarity_switch,[status(thm)],[36]) ).
thf(38,plain,
v3 != v0,
inference(lifteq,[status(thm)],[37]) ).
thf(1500,plain,
! [B: $i,A: $i] :
( ( ( v4 @ ( v3 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ~ $true
| ( v4 @ ( v2 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(paramod_ordered,[status(thm)],[1041,20]) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ( ( v4 @ ( v3 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ( v4 @ ( v2 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(simp,[status(thm)],[1500]) ).
thf(1502,plain,
( ( v3 @ ( v4 @ r ) )
| ( v4 @ ( v2 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(pattern_uni,[status(thm)],[1501:[bind(A,$thf( v3 )),bind(B,$thf( v4 ))]]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ r ) )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( B = C )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rno3cl) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ r ) )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( B = C )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1104,plain,
( ~ $true
| ( ( v2 @ ( v4 @ r ) )
!= ( v2 @ ( v3 @ r ) ) )
| ( v4 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[945]) ).
thf(1106,plain,
( ( ( v2 @ ( v4 @ r ) )
!= ( v2 @ ( v3 @ r ) ) )
| ( v4 @ ( v3 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(simp,[status(thm)],[1104]) ).
thf(5,axiom,
v0 != v2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv2) ).
thf(30,plain,
v0 != v2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
v0 != v2,
inference(polarity_switch,[status(thm)],[30]) ).
thf(32,plain,
v2 != v0,
inference(lifteq,[status(thm)],[31]) ).
thf(10,axiom,
v0 != v4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v0nv4) ).
thf(45,plain,
v0 != v4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(58,plain,
v0 != v5,
inference(polarity_switch,[status(thm)],[57]) ).
thf(59,plain,
v5 != v0,
inference(lifteq,[status(thm)],[58]) ).
thf(70,plain,
v4 != v5,
inference(polarity_switch,[status(thm)],[69]) ).
thf(71,plain,
v5 != v4,
inference(lifteq,[status(thm)],[70]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( B != v2 )
| ( A != v1 )
| ( C @ ( B @ r ) )
| ( C @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( B = C )
| ( A = C ) ),
inference(paramod_ordered,[status(thm)],[26,35]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( A != v1 )
| ( B @ ( v2 @ r ) )
| ( B @ ( A @ r ) )
| ( v2 @ ( A @ r ) )
| ( v2 = B )
| ( A = B ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( A )),bind(B,$thf( v2 ))]]) ).
thf(159,plain,
! [A: $i] :
( ( A @ ( v2 @ r ) )
| ( A @ ( v1 @ r ) )
| ( v2 @ ( v1 @ r ) )
| ( v2 = A )
| ( v1 = A ) ),
inference(simp,[status(thm)],[135]) ).
thf(11,axiom,
v1 != v4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1nv4) ).
thf(48,plain,
v1 != v4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(49,plain,
v1 != v4,
inference(polarity_switch,[status(thm)],[48]) ).
thf(50,plain,
v4 != v1,
inference(lifteq,[status(thm)],[49]) ).
thf(2901,plain,
! [B: $i,A: $i] :
( ( ( v5 @ ( v3 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ~ $true
| ( v5 @ ( v2 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(paramod_ordered,[status(thm)],[2783,20]) ).
thf(2902,plain,
! [B: $i,A: $i] :
( ( ( v5 @ ( v3 @ r ) )
!= ( B @ ( A @ r ) ) )
| ( A @ ( B @ r ) )
| ( v5 @ ( v2 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(simp,[status(thm)],[2901]) ).
thf(2903,plain,
( ( v3 @ ( v5 @ r ) )
| ( v5 @ ( v2 @ r ) )
| ( v2 @ ( v3 @ r ) ) ),
inference(pattern_uni,[status(thm)],[2902:[bind(A,$thf( v3 )),bind(B,$thf( v5 ))]]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ r ) )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( B = C )
| ( A = C )
| ( A = B ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ r ) )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( B = C )
| ( A = C )
| ( A = B ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(46,plain,
v0 != v4,
inference(polarity_switch,[status(thm)],[45]) ).
thf(47,plain,
v4 != v0,
inference(lifteq,[status(thm)],[46]) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] :
( ( B != v4 )
| ( C != v0 )
| ~ ( C @ ( B @ r ) )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( A = C )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[23,47]) ).
thf(769,plain,
! [B: $i,A: $i] :
( ( B != v0 )
| ~ ( B @ ( v4 @ r ) )
| ~ ( B @ ( A @ r ) )
| ~ ( v4 @ ( A @ r ) )
| ( A = B )
| ( A = v4 ) ),
inference(pattern_uni,[status(thm)],[768:[bind(A,$thf( A )),bind(B,$thf( v4 ))]]) ).
thf(808,plain,
! [A: $i] :
( ~ ( v0 @ ( v4 @ r ) )
| ~ ( v0 @ ( A @ r ) )
| ~ ( v4 @ ( A @ r ) )
| ( A = v0 )
| ( A = v4 ) ),
inference(simp,[status(thm)],[769]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( A != v2 )
| ( B != v1 )
| ( C @ ( B @ r ) )
| ( C @ ( A @ r ) )
| ( B @ ( A @ r ) )
| ( B = C )
| ( A = C ) ),
inference(paramod_ordered,[status(thm)],[26,35]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( A != v1 )
| ( B @ ( A @ r ) )
| ( B @ ( v2 @ r ) )
| ( A @ ( v2 @ r ) )
| ( A = B )
| ( v2 = B ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( v2 ))]]) ).
thf(158,plain,
! [A: $i] :
( ( A @ ( v1 @ r ) )
| ( A @ ( v2 @ r ) )
| ( v1 @ ( v2 @ r ) )
| ( v1 = A )
| ( v2 = A ) ),
inference(simp,[status(thm)],[133]) ).
thf(61,plain,
v1 != v5,
inference(polarity_switch,[status(thm)],[60]) ).
thf(62,plain,
v5 != v1,
inference(lifteq,[status(thm)],[61]) ).
thf(11847,plain,
$false,
inference(e,[status(thm)],[69,157,1016,41,39,66,35,1108,2783,1014,2309,1041,56,945,42,24,20,57,29,60,942,2296,38,1502,21,33,65,1106,156,53,32,45,44,59,27,71,54,159,48,63,50,2903,808,26,158,23,36,30,51,19,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA117-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 14:05:22 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.70/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.88/0.89 % [INFO] Parsing done (176ms).
% 1.05/0.90 % [INFO] Running in sequential loop mode.
% 1.61/1.30 % [INFO] eprover registered as external prover.
% 1.61/1.31 % [INFO] Scanning for conjecture ...
% 1.61/1.36 % [INFO] 18 axioms and no conjecture found.
% 1.77/1.42 % [INFO] Problem is propositional (TPTP CNF).
% 1.77/1.43 % [INFO] Type checking passed.
% 1.77/1.43 % [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 ...
% 27.01/6.28 % External prover 'e' found a proof!
% 27.01/6.28 % [INFO] Killing All external provers ...
% 27.01/6.29 % Time passed: 5800ms (effective reasoning time: 5375ms)
% 27.01/6.29 % Axioms used in derivation (18): v4nv5, v3nv4, v1nv4, v1nv2, v1nv5, rno3acl, v0nv1, v2nv4, v0nv5, rsym, v2nv3, v0nv4, v1nv3, v0nv3, v2nv5, v0nv2, rno3cl, v3nv5
% 27.01/6.29 % No. of inferences in proof: 121
% 27.01/6.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5800 ms resp. 5375 ms w/o parsing
% 23.18/6.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.18/6.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------