%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Wed Oct 7 10:20:43 AM UTC 2026
% Result : Unsatisfiable 25.82s 4.55s
% Output : CNFRefutation 25.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 540 ( 398 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 755 ( 113 ~; 180 |; 0 &; 462 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 136 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_sk_c1,type,
sk_c1: $i ).
thf(tp_sk_c2,type,
sk_c2: $i ).
thf(tp_sk_c3,type,
sk_c3: $i ).
thf(tp_sk_c4,type,
sk_c4: $i ).
thf(tp_sk_c5,type,
sk_c5: $i ).
thf(tp_sk_c6,type,
sk_c6: $i ).
thf(tp_sk_c7,type,
sk_c7: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(2,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(3,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
! [X3: $i,X4: $i,X2: $i,X1: $i,X5: $i] :
( ( ( multiply @ X3 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ X3 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ X4 )
!= sk_c6 )
| ( ( multiply @ X2 @ sk_c7 )
!= X1 )
| ( ( inverse @ X2 )
!= sk_c7 )
| ( ( multiply @ X5 @ X1 )
!= sk_c6 )
| ( ( inverse @ X5 )
!= X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
thf(7,negated_conjecture,
( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
thf(8,negated_conjecture,
( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
thf(9,negated_conjecture,
( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
thf(10,negated_conjecture,
( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
thf(11,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
thf(12,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
thf(13,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
thf(14,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
thf(15,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
thf(16,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
thf(17,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
thf(18,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
thf(19,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [X3: $i,X4: $i,X2: $i,X1: $i,X5: $i] :
( ( ( multiply @ X3 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ X3 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ X4 )
!= sk_c6 )
| ( ( multiply @ X2 @ sk_c7 )
!= X1 )
| ( ( inverse @ X2 )
!= sk_c7 )
| ( ( multiply @ X5 @ X1 )
!= sk_c6 )
| ( ( inverse @ X5 )
!= X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(32,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(33,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(34,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(35,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(36,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(37,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(38,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(39,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(40,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(41,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(42,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(43,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(44,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(45,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(46,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c3 )
= sk_c7 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(47,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(48,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
| ( ( inverse @ sk_c4 )
= sk_c5 ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(49,plain,
( ( ! [X3: $i,X4: $i,X2: $i,X1: $i,X5: $i] :
( ( ( multiply @ X3 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ X3 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ X4 )
!= sk_c6 )
| ( ( multiply @ X2 @ sk_c7 )
!= X1 )
| ( ( inverse @ X2 )
!= sk_c7 )
| ( ( multiply @ X5 @ X1 )
!= sk_c6 )
| ( ( inverse @ X5 )
!= X1 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(50,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(51,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(53,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[36]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( multiply @ SX0 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ SX0 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ SX1 )
!= sk_c6 )
| ( ( multiply @ SX2 @ sk_c7 )
!= SX3 )
| ( ( inverse @ SX2 )
!= sk_c7 )
| ( ( multiply @ SX4 @ SX3 )
!= sk_c6 )
| ( ( inverse @ SX4 )
!= SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(55,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(56,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c3 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(57,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(58,plain,
( ( ( ( multiply @ sk_c1 @ sk_c7 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c4 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(59,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(60,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( inverse @ sk_c3 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(61,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(62,plain,
( ( ( ( inverse @ sk_c1 )
= sk_c7 )
= $true )
| ( ( ( inverse @ sk_c4 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(63,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c3 @ sk_c7 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(64,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c3 )
= sk_c7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(65,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( multiply @ sk_c4 @ sk_c5 )
= sk_c6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(66,plain,
( ( ( ( multiply @ sk_c7 @ sk_c2 )
= sk_c6 )
= $true )
| ( ( ( inverse @ sk_c4 )
= sk_c5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(67,plain,
! [SV1: $i] :
( ( ( multiply @ identity @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
! [SV2: $i] :
( ( ( multiply @ ( inverse @ SV2 ) @ SV2 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV3: $i] :
( ( ! [SY10: $i,SY11: $i] :
( ( multiply @ ( multiply @ SV3 @ SY10 ) @ SY11 )
= ( multiply @ SV3 @ ( multiply @ SY10 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(71,plain,
! [SV4: $i] :
( ( ! [SY12: $i,SY13: $i,SY14: $i,SY15: $i] :
( ( ( multiply @ SV4 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ SV4 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ SY12 )
!= sk_c6 )
| ( ( multiply @ SY13 @ sk_c7 )
!= SY14 )
| ( ( inverse @ SY13 )
!= sk_c7 )
| ( ( multiply @ SY15 @ SY14 )
!= sk_c6 )
| ( ( inverse @ SY15 )
!= SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(72,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY16: $i] :
( ( multiply @ ( multiply @ SV3 @ SV5 ) @ SY16 )
= ( multiply @ SV3 @ ( multiply @ SV5 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV6: $i,SV4: $i] :
( ( ! [SY17: $i,SY18: $i,SY19: $i] :
( ( ( multiply @ SV4 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ SV4 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
| ( ( multiply @ SY17 @ sk_c7 )
!= SY18 )
| ( ( inverse @ SY17 )
!= sk_c7 )
| ( ( multiply @ SY19 @ SY18 )
!= sk_c6 )
| ( ( inverse @ SY19 )
!= SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( multiply @ ( multiply @ SV3 @ SV5 ) @ SV7 )
= ( multiply @ SV3 @ ( multiply @ SV5 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(75,plain,
! [SV8: $i,SV6: $i,SV4: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ( ( multiply @ SV4 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ SV4 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
| ( ( multiply @ SV8 @ sk_c7 )
!= SY20 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SY21 @ SY20 )
!= sk_c6 )
| ( ( inverse @ SY21 )
!= SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(76,plain,
! [SV9: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ! [SY22: $i] :
( ( ( multiply @ SV4 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ SV4 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
| ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SY22 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SY22 )
!= SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(77,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( ( multiply @ SV4 @ sk_c7 )
!= sk_c6 )
| ( ( inverse @ SV4 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
| ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(78,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( ( multiply @ SV4 @ sk_c7 )
!= sk_c6 )
= $true )
| ( ( ( ( inverse @ SV4 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
| ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(79,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false )
| ( ( ( ( inverse @ SV4 )
!= sk_c7 )
| ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
| ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(80,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( ( inverse @ SV4 )
!= sk_c7 )
= $true )
| ( ( ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
| ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(81,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
| ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(82,plain,
! [SV4: $i,SV10: $i,SV9: $i,SV8: $i,SV6: $i] :
( ( ( ( multiply @ sk_c7 @ SV6 )
!= sk_c6 )
= $true )
| ( ( ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(83,plain,
! [SV4: $i,SV10: $i,SV9: $i,SV8: $i,SV6: $i] :
( ( ( ( multiply @ sk_c7 @ SV6 )
= sk_c6 )
= $false )
| ( ( ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
| ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(84,plain,
! [SV4: $i,SV6: $i,SV10: $i,SV9: $i,SV8: $i] :
( ( ( ( multiply @ SV8 @ sk_c7 )
!= SV9 )
= $true )
| ( ( ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true )
| ( ( ( multiply @ sk_c7 @ SV6 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(85,plain,
! [SV4: $i,SV6: $i,SV10: $i,SV9: $i,SV8: $i] :
( ( ( ( multiply @ SV8 @ sk_c7 )
= SV9 )
= $false )
| ( ( ( ( inverse @ SV8 )
!= sk_c7 )
| ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true )
| ( ( ( multiply @ sk_c7 @ SV6 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(86,plain,
! [SV4: $i,SV6: $i,SV9: $i,SV10: $i,SV8: $i] :
( ( ( ( inverse @ SV8 )
!= sk_c7 )
= $true )
| ( ( ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true )
| ( ( ( multiply @ SV8 @ sk_c7 )
= SV9 )
= $false )
| ( ( ( multiply @ sk_c7 @ SV6 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(87,plain,
! [SV4: $i,SV6: $i,SV9: $i,SV10: $i,SV8: $i] :
( ( ( ( inverse @ SV8 )
= sk_c7 )
= $false )
| ( ( ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
| ( ( inverse @ SV10 )
!= SV9 ) )
= $true )
| ( ( ( multiply @ SV8 @ sk_c7 )
= SV9 )
= $false )
| ( ( ( multiply @ sk_c7 @ SV6 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(88,plain,
! [SV4: $i,SV6: $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( multiply @ SV10 @ SV9 )
!= sk_c6 )
= $true )
| ( ( ( inverse @ SV10 )
!= SV9 )
= $true )
| ( ( ( inverse @ SV8 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV8 @ sk_c7 )
= SV9 )
= $false )
| ( ( ( multiply @ sk_c7 @ SV6 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(89,plain,
! [SV4: $i,SV6: $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( multiply @ SV10 @ SV9 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV10 )
!= SV9 )
= $true )
| ( ( ( inverse @ SV8 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV8 @ sk_c7 )
= SV9 )
= $false )
| ( ( ( multiply @ sk_c7 @ SV6 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(90,plain,
! [SV4: $i,SV6: $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( inverse @ SV10 )
= SV9 )
= $false )
| ( ( ( multiply @ SV10 @ SV9 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV8 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV8 @ sk_c7 )
= SV9 )
= $false )
| ( ( ( multiply @ sk_c7 @ SV6 )
= sk_c6 )
= $false )
| ( ( ( inverse @ SV4 )
= sk_c7 )
= $false )
| ( ( ( multiply @ SV4 @ sk_c7 )
= sk_c6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(91,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,90,74,70,68,67,66,65,64,63,62,61,60,59,58,57,56]) ).
thf(92,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n016.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 10:43:29 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.82/4.55
% 25.82/4.55 No.of.Axioms: 16
% 25.82/4.55
% 25.82/4.55 Length.of.Defs: 0
% 25.82/4.55
% 25.82/4.55 Contains.Choice.Funs: false
% 25.82/4.55 ..
% 25.82/4.55
% 25.82/4.55 ********************************
% 25.82/4.55 * All subproblems solved! *
% 25.82/4.55 ********************************
% 25.82/4.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:91,loop_count:0,foatp_calls:1,translation:fof_full)
% 25.82/4.55
% 25.82/4.55 %**** Beginning of derivation protocol ****
% 25.82/4.55 % SZS output start CNFRefutation
% See solution above
% 25.82/4.55
% 25.82/4.55 %**** End of derivation protocol ****
% 25.82/4.55 %**** no. of clauses in derivation: 92 ****
% 25.82/4.55 %**** clause counter: 91 ****
% 25.82/4.55
% 25.82/4.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:91,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------