%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KLE129+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n014.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 10:26:01 AM UTC 2026
% Result : Theorem 2.59s 0.61s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 92 ( 81 unt; 0 typ; 0 def)
% Number of atoms : 315 ( 209 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 878 ( 44 ~; 35 |; 0 &; 781 @)
% ( 3 <=>; 9 =>; 6 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 171 ( 0 ^; 171 !; 0 ?; 171 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
thf(tp_antidomain,type,
antidomain: $i > $i ).
thf(tp_backward_box,type,
backward_box: $i > $i > $i ).
thf(tp_backward_diamond,type,
backward_diamond: $i > $i > $i ).
thf(tp_c,type,
c: $i > $i ).
thf(tp_coantidomain,type,
coantidomain: $i > $i ).
thf(tp_codomain,type,
codomain: $i > $i ).
thf(tp_divergence,type,
divergence: $i > $i ).
thf(tp_domain,type,
domain: $i > $i ).
thf(tp_domain_difference,type,
domain_difference: $i > $i > $i ).
thf(tp_forward_box,type,
forward_box: $i > $i > $i ).
thf(tp_forward_diamond,type,
forward_diamond: $i > $i > $i ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_multiplication,type,
multiplication: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(tp_star,type,
star: $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( addition @ ( domain @ X0 ) @ ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
= ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
=> ( ( addition @ ( domain @ X0 ) @ ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) )
= ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence2) ).
thf(2,axiom,
! [X0: $i] :
( ( forward_diamond @ X0 @ ( divergence @ X0 ) )
= ( divergence @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
thf(6,axiom,
! [X0: $i,X1: $i] :
( ( forward_diamond @ X0 @ X1 )
= ( domain @ ( multiplication @ X0 @ ( domain @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
thf(13,axiom,
! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(18,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(19,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(25,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(26,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(29,conjecture,
! [X0: $i] :
( ( ( divergence @ X0 )
= zero )
<= ! [X1: $i] :
( ( ( addition @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) )
= ( forward_diamond @ X0 @ ( domain @ X1 ) ) )
=> ( ( domain @ X1 )
= zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(30,negated_conjecture,
( ( ! [X0: $i] :
( ( ( divergence @ X0 )
= zero )
<= ! [X1: $i] :
( ( ( addition @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) )
= ( forward_diamond @ X0 @ ( domain @ X1 ) ) )
=> ( ( domain @ X1 )
= zero ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [X0: $i] :
( ( ( divergence @ X0 )
= zero )
<= ! [X1: $i] :
( ( ( addition @ ( domain @ X1 ) @ ( forward_diamond @ X0 @ ( domain @ X1 ) ) )
= ( forward_diamond @ X0 @ ( domain @ X1 ) ) )
=> ( ( domain @ X1 )
= zero ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( addition @ ( domain @ X0 ) @ ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
= ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
=> ( ( addition @ ( domain @ X0 ) @ ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) )
= ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
( ( ! [X0: $i] :
( ( forward_diamond @ X0 @ ( divergence @ X0 ) )
= ( divergence @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(34,plain,
( ( ! [X0: $i,X1: $i] :
( ( forward_diamond @ X0 @ X1 )
= ( domain @ ( multiplication @ X0 @ ( domain @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(35,plain,
( ( ! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(43,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(45,plain,
( ( ( ( divergence @ sK1_X0 )
= zero )
<= ! [SY26: $i] :
( ( ( addition @ ( domain @ SY26 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY26 ) ) )
= ( forward_diamond @ sK1_X0 @ ( domain @ SY26 ) ) )
=> ( ( domain @ SY26 )
= zero ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(46,plain,
( ( ~ ( ( ( divergence @ sK1_X0 )
= zero )
<= ! [SY26: $i] :
( ( ( addition @ ( domain @ SY26 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY26 ) ) )
= ( forward_diamond @ sK1_X0 @ ( domain @ SY26 ) ) )
=> ( ( domain @ SY26 )
= zero ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(48,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( addition @ A @ zero )
= A ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( addition @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(51,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(52,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(56,plain,
( ( ! [X0: $i] :
( ( domain @ X0 )
= ( antidomain @ ( antidomain @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(57,plain,
( ( ! [X0: $i,X1: $i] :
( ( forward_diamond @ X0 @ X1 )
= ( domain @ ( multiplication @ X0 @ ( domain @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(58,plain,
( ( ! [X0: $i] :
( ( forward_diamond @ X0 @ ( divergence @ X0 ) )
= ( divergence @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(59,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( addition @ ( domain @ X0 ) @ ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
= ( addition @ ( forward_diamond @ X1 @ ( domain @ X0 ) ) @ ( domain @ X2 ) ) )
=> ( ( addition @ ( domain @ X0 ) @ ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) )
= ( addition @ ( divergence @ X1 ) @ ( forward_diamond @ ( star @ X1 ) @ ( domain @ X2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(60,plain,
( ( ~ ( ( ( divergence @ sK1_X0 )
= zero )
<= ! [SY26: $i] :
( ( ( addition @ ( domain @ SY26 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SY26 ) ) )
= ( forward_diamond @ sK1_X0 @ ( domain @ SY26 ) ) )
=> ( ( domain @ SY26 )
= zero ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( addition @ ( domain @ SX0 ) @ ( addition @ ( forward_diamond @ SX1 @ ( domain @ SX0 ) ) @ ( domain @ SX2 ) ) )
!= ( addition @ ( forward_diamond @ SX1 @ ( domain @ SX0 ) ) @ ( domain @ SX2 ) ) )
| ( ( addition @ ( domain @ SX0 ) @ ( addition @ ( divergence @ SX1 ) @ ( forward_diamond @ ( star @ SX1 ) @ ( domain @ SX2 ) ) ) )
= ( addition @ ( divergence @ SX1 ) @ ( forward_diamond @ ( star @ SX1 ) @ ( domain @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(62,plain,
( ( ~ ( ( ( divergence @ sK1_X0 )
= zero )
| ~ ! [SX0: $i] :
( ( ( addition @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) )
!= ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) )
| ( ( domain @ SX0 )
= zero ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(63,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) )
| ~ ( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(64,plain,
! [SV1: $i] :
( ( ! [SY27: $i] :
( ( addition @ SV1 @ SY27 )
= ( addition @ SY27 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(65,plain,
! [SV2: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( addition @ SY29 @ ( addition @ SY28 @ SV2 ) )
= ( addition @ ( addition @ SY29 @ SY28 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(66,plain,
! [SV3: $i] :
( ( ( addition @ SV3 @ zero )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(67,plain,
! [SV4: $i] :
( ( ( addition @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
! [SV5: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ( multiplication @ SV5 @ ( addition @ SY30 @ SY31 ) )
= ( addition @ ( multiplication @ SV5 @ SY30 ) @ ( multiplication @ SV5 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV6: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ( multiplication @ ( addition @ SV6 @ SY32 ) @ SY33 )
= ( addition @ ( multiplication @ SV6 @ SY33 ) @ ( multiplication @ SY32 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV7: $i] :
( ( ( multiplication @ SV7 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(71,plain,
! [SV8: $i] :
( ( ( multiplication @ zero @ SV8 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(72,plain,
! [SV9: $i] :
( ( ( domain @ SV9 )
= ( antidomain @ ( antidomain @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(73,plain,
! [SV10: $i] :
( ( ! [SY34: $i] :
( ( forward_diamond @ SV10 @ SY34 )
= ( domain @ ( multiplication @ SV10 @ ( domain @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(74,plain,
! [SV11: $i] :
( ( ( forward_diamond @ SV11 @ ( divergence @ SV11 ) )
= ( divergence @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(75,plain,
! [SV12: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( forward_diamond @ SY35 @ ( domain @ SV12 ) ) @ ( domain @ SY36 ) ) )
!= ( addition @ ( forward_diamond @ SY35 @ ( domain @ SV12 ) ) @ ( domain @ SY36 ) ) )
| ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( divergence @ SY35 ) @ ( forward_diamond @ ( star @ SY35 ) @ ( domain @ SY36 ) ) ) )
= ( addition @ ( divergence @ SY35 ) @ ( forward_diamond @ ( star @ SY35 ) @ ( domain @ SY36 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(76,plain,
( ( ( ( divergence @ sK1_X0 )
= zero )
| ~ ! [SX0: $i] :
( ( ( addition @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) )
!= ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) )
| ( ( domain @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(77,plain,
! [SV13: $i] :
( ( ! [SY37: $i] :
~ ( ~ ( ~ ( leq @ SV13 @ SY37 )
| ( ( addition @ SV13 @ SY37 )
= SY37 ) )
| ~ ( ( ( addition @ SV13 @ SY37 )
!= SY37 )
| ( leq @ SV13 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(78,plain,
! [SV14: $i,SV1: $i] :
( ( ( addition @ SV1 @ SV14 )
= ( addition @ SV14 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(79,plain,
! [SV2: $i,SV15: $i] :
( ( ! [SY38: $i] :
( ( addition @ SY38 @ ( addition @ SV15 @ SV2 ) )
= ( addition @ ( addition @ SY38 @ SV15 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(80,plain,
! [SV16: $i,SV5: $i] :
( ( ! [SY39: $i] :
( ( multiplication @ SV5 @ ( addition @ SV16 @ SY39 ) )
= ( addition @ ( multiplication @ SV5 @ SV16 ) @ ( multiplication @ SV5 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(81,plain,
! [SV17: $i,SV6: $i] :
( ( ! [SY40: $i] :
( ( multiplication @ ( addition @ SV6 @ SV17 ) @ SY40 )
= ( addition @ ( multiplication @ SV6 @ SY40 ) @ ( multiplication @ SV17 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV18: $i,SV10: $i] :
( ( ( forward_diamond @ SV10 @ SV18 )
= ( domain @ ( multiplication @ SV10 @ ( domain @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV19: $i,SV12: $i] :
( ( ! [SY41: $i] :
( ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( forward_diamond @ SV19 @ ( domain @ SV12 ) ) @ ( domain @ SY41 ) ) )
!= ( addition @ ( forward_diamond @ SV19 @ ( domain @ SV12 ) ) @ ( domain @ SY41 ) ) )
| ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( divergence @ SV19 ) @ ( forward_diamond @ ( star @ SV19 ) @ ( domain @ SY41 ) ) ) )
= ( addition @ ( divergence @ SV19 ) @ ( forward_diamond @ ( star @ SV19 ) @ ( domain @ SY41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(84,plain,
( ( ( divergence @ sK1_X0 )
= zero )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(85,plain,
( ( ~ ! [SX0: $i] :
( ( ( addition @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) )
!= ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) )
| ( ( domain @ SX0 )
= zero ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV20: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( leq @ SV13 @ SV20 )
| ( ( addition @ SV13 @ SV20 )
= SV20 ) )
| ~ ( ( ( addition @ SV13 @ SV20 )
!= SV20 )
| ( leq @ SV13 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV2: $i,SV15: $i,SV21: $i] :
( ( ( addition @ SV21 @ ( addition @ SV15 @ SV2 ) )
= ( addition @ ( addition @ SV21 @ SV15 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV22: $i,SV16: $i,SV5: $i] :
( ( ( multiplication @ SV5 @ ( addition @ SV16 @ SV22 ) )
= ( addition @ ( multiplication @ SV5 @ SV16 ) @ ( multiplication @ SV5 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV23: $i,SV17: $i,SV6: $i] :
( ( ( multiplication @ ( addition @ SV6 @ SV17 ) @ SV23 )
= ( addition @ ( multiplication @ SV6 @ SV23 ) @ ( multiplication @ SV17 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV24: $i,SV19: $i,SV12: $i] :
( ( ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( forward_diamond @ SV19 @ ( domain @ SV12 ) ) @ ( domain @ SV24 ) ) )
!= ( addition @ ( forward_diamond @ SV19 @ ( domain @ SV12 ) ) @ ( domain @ SV24 ) ) )
| ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( divergence @ SV19 ) @ ( forward_diamond @ ( star @ SV19 ) @ ( domain @ SV24 ) ) ) )
= ( addition @ ( divergence @ SV19 ) @ ( forward_diamond @ ( star @ SV19 ) @ ( domain @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(91,plain,
( ( ! [SX0: $i] :
( ( ( addition @ ( domain @ SX0 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) )
!= ( forward_diamond @ sK1_X0 @ ( domain @ SX0 ) ) )
| ( ( domain @ SX0 )
= zero ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(92,plain,
! [SV20: $i,SV13: $i] :
( ( ~ ( ~ ( leq @ SV13 @ SV20 )
| ( ( addition @ SV13 @ SV20 )
= SV20 ) )
| ~ ( ( ( addition @ SV13 @ SV20 )
!= SV20 )
| ( leq @ SV13 @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV24: $i,SV19: $i,SV12: $i] :
( ( ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( forward_diamond @ SV19 @ ( domain @ SV12 ) ) @ ( domain @ SV24 ) ) )
!= ( addition @ ( forward_diamond @ SV19 @ ( domain @ SV12 ) ) @ ( domain @ SV24 ) ) )
= $true )
| ( ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( divergence @ SV19 ) @ ( forward_diamond @ ( star @ SV19 ) @ ( domain @ SV24 ) ) ) )
= ( addition @ ( divergence @ SV19 ) @ ( forward_diamond @ ( star @ SV19 ) @ ( domain @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV25: $i] :
( ( ( ( addition @ ( domain @ SV25 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SV25 ) ) )
!= ( forward_diamond @ sK1_X0 @ ( domain @ SV25 ) ) )
| ( ( domain @ SV25 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV20: $i,SV13: $i] :
( ( ~ ( ~ ( leq @ SV13 @ SV20 )
| ( ( addition @ SV13 @ SV20 )
= SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(96,plain,
! [SV20: $i,SV13: $i] :
( ( ~ ( ( ( addition @ SV13 @ SV20 )
!= SV20 )
| ( leq @ SV13 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(97,plain,
! [SV24: $i,SV19: $i,SV12: $i] :
( ( ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( forward_diamond @ SV19 @ ( domain @ SV12 ) ) @ ( domain @ SV24 ) ) )
= ( addition @ ( forward_diamond @ SV19 @ ( domain @ SV12 ) ) @ ( domain @ SV24 ) ) )
= $false )
| ( ( ( addition @ ( domain @ SV12 ) @ ( addition @ ( divergence @ SV19 ) @ ( forward_diamond @ ( star @ SV19 ) @ ( domain @ SV24 ) ) ) )
= ( addition @ ( divergence @ SV19 ) @ ( forward_diamond @ ( star @ SV19 ) @ ( domain @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV25: $i] :
( ( ( ( addition @ ( domain @ SV25 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SV25 ) ) )
!= ( forward_diamond @ sK1_X0 @ ( domain @ SV25 ) ) )
= $true )
| ( ( ( domain @ SV25 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV20: $i,SV13: $i] :
( ( ~ ( leq @ SV13 @ SV20 )
| ( ( addition @ SV13 @ SV20 )
= SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(100,plain,
! [SV20: $i,SV13: $i] :
( ( ( ( addition @ SV13 @ SV20 )
!= SV20 )
| ( leq @ SV13 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(101,plain,
! [SV25: $i] :
( ( ( ( addition @ ( domain @ SV25 ) @ ( forward_diamond @ sK1_X0 @ ( domain @ SV25 ) ) )
= ( forward_diamond @ sK1_X0 @ ( domain @ SV25 ) ) )
= $false )
| ( ( ( domain @ SV25 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV20: $i,SV13: $i] :
( ( ( ~ ( leq @ SV13 @ SV20 ) )
= $true )
| ( ( ( addition @ SV13 @ SV20 )
= SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(103,plain,
! [SV20: $i,SV13: $i] :
( ( ( ( addition @ SV13 @ SV20 )
!= SV20 )
= $true )
| ( ( leq @ SV13 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV20: $i,SV13: $i] :
( ( ( leq @ SV13 @ SV20 )
= $false )
| ( ( ( addition @ SV13 @ SV20 )
= SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(105,plain,
! [SV20: $i,SV13: $i] :
( ( ( ( addition @ SV13 @ SV20 )
= SV20 )
= $false )
| ( ( leq @ SV13 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(106,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[66,105,104,101,97,89,88,87,84,82,78,74,72,71,70,67]) ).
thf(107,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE129+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.17 % Computer : n014.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 11:35:56 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.59/0.61
% 2.59/0.61 No.of.Axioms: 13
% 2.59/0.61
% 2.59/0.61 Length.of.Defs: 0
% 2.59/0.61
% 2.59/0.61 Contains.Choice.Funs: false
% 2.59/0.61 ...
% 2.59/0.61
% 2.59/0.61 ********************************
% 2.59/0.61 * All subproblems solved! *
% 2.59/0.61 ********************************
% 2.59/0.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:106,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.59/0.61
% 2.59/0.61 %**** Beginning of derivation protocol ****
% 2.59/0.61 % SZS output start CNFRefutation
% See solution above
% 2.59/0.61
% 2.59/0.61 %**** End of derivation protocol ****
% 2.59/0.61 %**** no. of clauses in derivation: 92 ****
% 2.59/0.61 %**** clause counter: 106 ****
% 2.59/0.61
% 2.59/0.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:106,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------