%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP748+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 : n017.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 10:21:52 AM UTC 2026
% Result : Theorem 27.31s 4.81s
% Output : CNFRefutation 27.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 76 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 171 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 840 ( 2 ~; 27 |; 0 &; 811 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 207 ( 0 ^; 207 !; 0 ?; 207 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_i,type,
i: $i > $i ).
thf(tp_ld,type,
ld: $i > $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_rd,type,
rd: $i > $i > $i ).
thf(tp_sK10_SY49,type,
sK10_SY49: $i ).
thf(tp_sK11_SY50,type,
sK11_SY50: $i ).
thf(tp_sK12_SY51,type,
sK12_SY51: $i ).
thf(tp_sK1_X9,type,
sK1_X9: $i ).
thf(tp_sK2_X6,type,
sK2_X6: $i ).
thf(tp_sK3_SY40,type,
sK3_SY40: $i ).
thf(tp_sK4_X0,type,
sK4_X0: $i ).
thf(tp_sK5_X3,type,
sK5_X3: $i ).
thf(tp_sK6_SY42,type,
sK6_SY42: $i ).
thf(tp_sK7_SY44,type,
sK7_SY44: $i ).
thf(tp_sK8_SY45,type,
sK8_SY45: $i ).
thf(tp_sK9_SY47,type,
sK9_SY47: $i ).
thf(tp_unit,type,
unit: $i ).
thf(1,axiom,
! [B: $i,A: $i] :
( ( ( mult @ A @ B )
= ( mult @ B @ A ) )
| ( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
thf(2,axiom,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
thf(3,axiom,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( i @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(6,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(12,conjecture,
( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) )
| ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) )
| ! [X6: $i,X7: $i,X8: $i] :
( ( mult @ ( mult @ X8 @ X6 ) @ ( mult @ X7 @ X8 ) )
= ( mult @ ( mult @ X8 @ ( mult @ X6 @ X7 ) ) @ X8 ) )
| ! [X9: $i,X10: $i,X11: $i] :
( ( mult @ ( mult @ X11 @ X9 ) @ ( mult @ X10 @ X11 ) )
= ( mult @ X11 @ ( mult @ ( mult @ X9 @ X10 ) @ X11 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(13,negated_conjecture,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) )
| ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) )
| ! [X6: $i,X7: $i,X8: $i] :
( ( mult @ ( mult @ X8 @ X6 ) @ ( mult @ X7 @ X8 ) )
= ( mult @ ( mult @ X8 @ ( mult @ X6 @ X7 ) ) @ X8 ) )
| ! [X9: $i,X10: $i,X11: $i] :
( ( mult @ ( mult @ X11 @ X9 ) @ ( mult @ X10 @ X11 ) )
= ( mult @ X11 @ ( mult @ ( mult @ X9 @ X10 ) @ X11 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) )
| ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) )
| ! [X6: $i,X7: $i,X8: $i] :
( ( mult @ ( mult @ X8 @ X6 ) @ ( mult @ X7 @ X8 ) )
= ( mult @ ( mult @ X8 @ ( mult @ X6 @ X7 ) ) @ X8 ) )
| ! [X9: $i,X10: $i,X11: $i] :
( ( mult @ ( mult @ X11 @ X9 ) @ ( mult @ X10 @ X11 ) )
= ( mult @ X11 @ ( mult @ ( mult @ X9 @ X10 ) @ X11 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [B: $i,A: $i] :
( ( ( mult @ A @ B )
= ( mult @ B @ A ) )
| ( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( i @ B ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ~ ( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) )
| ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) )
| ! [X6: $i,X7: $i,X8: $i] :
( ( mult @ ( mult @ X8 @ X6 ) @ ( mult @ X7 @ X8 ) )
= ( mult @ ( mult @ X8 @ ( mult @ X6 @ X7 ) ) @ X8 ) )
| ! [X9: $i,X10: $i,X11: $i] :
( ( mult @ ( mult @ X11 @ X9 ) @ ( mult @ X10 @ X11 ) )
= ( mult @ X11 @ ( mult @ ( mult @ X9 @ X10 ) @ X11 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(28,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(33,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(34,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( i @ B ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(37,plain,
( ( ! [B: $i,A: $i] :
( ( ( mult @ A @ B )
= ( mult @ B @ A ) )
| ( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(38,plain,
( ( ~ ( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) )
| ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) )
| ! [X6: $i,X7: $i,X8: $i] :
( ( mult @ ( mult @ X8 @ X6 ) @ ( mult @ X7 @ X8 ) )
= ( mult @ ( mult @ X8 @ ( mult @ X6 @ X7 ) ) @ X8 ) )
| ! [X9: $i,X10: $i,X11: $i] :
( ( mult @ ( mult @ X11 @ X9 ) @ ( mult @ X10 @ X11 ) )
= ( mult @ X11 @ ( mult @ ( mult @ X9 @ X10 ) @ X11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(39,plain,
! [SV1: $i] :
( ( ! [SY31: $i] :
( ( mult @ SY31 @ ( ld @ SY31 @ SV1 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(40,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
( ( ld @ SY32 @ ( mult @ SY32 @ SV2 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(41,plain,
! [SV3: $i] :
( ( ! [SY33: $i] :
( ( mult @ ( rd @ SY33 @ SV3 ) @ SV3 )
= SY33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(42,plain,
! [SV4: $i] :
( ( ! [SY34: $i] :
( ( rd @ ( mult @ SY34 @ SV4 ) @ SV4 )
= SY34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(43,plain,
! [SV5: $i] :
( ( ( mult @ SV5 @ unit )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(44,plain,
! [SV6: $i] :
( ( ( mult @ unit @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(45,plain,
! [SV7: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ( mult @ ( mult @ ( mult @ SY36 @ SY35 ) @ SV7 ) @ SY35 )
= ( mult @ SY36 @ ( mult @ ( mult @ SY35 @ SV7 ) @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(46,plain,
! [SV8: $i] :
( ( ! [SY37: $i] :
( ( mult @ ( mult @ SY37 @ SV8 ) @ ( i @ SV8 ) )
= SY37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(47,plain,
! [SV9: $i] :
( ( ( mult @ SV9 @ ( i @ SV9 ) )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(48,plain,
! [SV10: $i] :
( ( ( mult @ ( i @ SV10 ) @ SV10 )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(49,plain,
! [SV11: $i] :
( ( ! [SY38: $i] :
( ( ( mult @ SY38 @ SV11 )
= ( mult @ SV11 @ SY38 ) )
| ( ( mult @ ( i @ SY38 ) @ ( mult @ SY38 @ SV11 ) )
= SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(50,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) )
| ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) )
| ! [X6: $i,X7: $i,X8: $i] :
( ( mult @ ( mult @ X8 @ X6 ) @ ( mult @ X7 @ X8 ) )
= ( mult @ ( mult @ X8 @ ( mult @ X6 @ X7 ) ) @ X8 ) )
| ! [X9: $i,X10: $i,X11: $i] :
( ( mult @ ( mult @ X11 @ X9 ) @ ( mult @ X10 @ X11 ) )
= ( mult @ X11 @ ( mult @ ( mult @ X9 @ X10 ) @ X11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(51,plain,
! [SV1: $i,SV12: $i] :
( ( ( mult @ SV12 @ ( ld @ SV12 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(52,plain,
! [SV2: $i,SV13: $i] :
( ( ( ld @ SV13 @ ( mult @ SV13 @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(53,plain,
! [SV3: $i,SV14: $i] :
( ( ( mult @ ( rd @ SV14 @ SV3 ) @ SV3 )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(54,plain,
! [SV4: $i,SV15: $i] :
( ( ( rd @ ( mult @ SV15 @ SV4 ) @ SV4 )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(55,plain,
! [SV7: $i,SV16: $i] :
( ( ! [SY39: $i] :
( ( mult @ ( mult @ ( mult @ SY39 @ SV16 ) @ SV7 ) @ SV16 )
= ( mult @ SY39 @ ( mult @ ( mult @ SV16 @ SV7 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV8: $i,SV17: $i] :
( ( ( mult @ ( mult @ SV17 @ SV8 ) @ ( i @ SV8 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(57,plain,
! [SV11: $i,SV18: $i] :
( ( ( ( mult @ SV18 @ SV11 )
= ( mult @ SV11 @ SV18 ) )
| ( ( mult @ ( i @ SV18 ) @ ( mult @ SV18 @ SV11 ) )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) )
| ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) )
| ! [X6: $i,X7: $i,X8: $i] :
( ( mult @ ( mult @ X8 @ X6 ) @ ( mult @ X7 @ X8 ) )
= ( mult @ ( mult @ X8 @ ( mult @ X6 @ X7 ) ) @ X8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(59,plain,
( ( ! [X9: $i,X10: $i,X11: $i] :
( ( mult @ ( mult @ X11 @ X9 ) @ ( mult @ X10 @ X11 ) )
= ( mult @ X11 @ ( mult @ ( mult @ X9 @ X10 ) @ X11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(60,plain,
! [SV7: $i,SV16: $i,SV19: $i] :
( ( ( mult @ ( mult @ ( mult @ SV19 @ SV16 ) @ SV7 ) @ SV16 )
= ( mult @ SV19 @ ( mult @ ( mult @ SV16 @ SV7 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV11: $i,SV18: $i] :
( ( ( ( mult @ SV18 @ SV11 )
= ( mult @ SV11 @ SV18 ) )
= $true )
| ( ( ( mult @ ( i @ SV18 ) @ ( mult @ SV18 @ SV11 ) )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) )
| ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(63,plain,
( ( ! [X6: $i,X7: $i,X8: $i] :
( ( mult @ ( mult @ X8 @ X6 ) @ ( mult @ X7 @ X8 ) )
= ( mult @ ( mult @ X8 @ ( mult @ X6 @ X7 ) ) @ X8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(64,plain,
( ( ! [SY40: $i,SY41: $i] :
( ( mult @ ( mult @ SY41 @ sK1_X9 ) @ ( mult @ SY40 @ SY41 ) )
= ( mult @ SY41 @ ( mult @ ( mult @ sK1_X9 @ SY40 ) @ SY41 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(65,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X2 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( mult @ ( mult @ X2 @ X0 ) @ X2 ) @ X1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(66,plain,
( ( ! [X3: $i,X4: $i,X5: $i] :
( ( mult @ X3 @ ( mult @ X5 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ ( mult @ ( mult @ X3 @ X5 ) @ X4 ) @ X5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( mult @ ( mult @ SY43 @ sK2_X6 ) @ ( mult @ SY42 @ SY43 ) )
= ( mult @ ( mult @ SY43 @ ( mult @ sK2_X6 @ SY42 ) ) @ SY43 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(68,plain,
( ( ! [SY44: $i] :
( ( mult @ ( mult @ SY44 @ sK1_X9 ) @ ( mult @ sK3_SY40 @ SY44 ) )
= ( mult @ SY44 @ ( mult @ ( mult @ sK1_X9 @ sK3_SY40 ) @ SY44 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(69,plain,
( ( ! [SY45: $i,SY46: $i] :
( ( mult @ SY46 @ ( mult @ sK4_X0 @ ( mult @ SY46 @ SY45 ) ) )
= ( mult @ ( mult @ ( mult @ SY46 @ sK4_X0 ) @ SY46 ) @ SY45 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(70,plain,
( ( ! [SY47: $i,SY48: $i] :
( ( mult @ sK5_X3 @ ( mult @ SY48 @ ( mult @ SY47 @ SY48 ) ) )
= ( mult @ ( mult @ ( mult @ sK5_X3 @ SY48 ) @ SY47 ) @ SY48 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(71,plain,
( ( ! [SY49: $i] :
( ( mult @ ( mult @ SY49 @ sK2_X6 ) @ ( mult @ sK6_SY42 @ SY49 ) )
= ( mult @ ( mult @ SY49 @ ( mult @ sK2_X6 @ sK6_SY42 ) ) @ SY49 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(72,plain,
( ( ( mult @ ( mult @ sK7_SY44 @ sK1_X9 ) @ ( mult @ sK3_SY40 @ sK7_SY44 ) )
= ( mult @ sK7_SY44 @ ( mult @ ( mult @ sK1_X9 @ sK3_SY40 ) @ sK7_SY44 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(73,plain,
( ( ! [SY50: $i] :
( ( mult @ SY50 @ ( mult @ sK4_X0 @ ( mult @ SY50 @ sK8_SY45 ) ) )
= ( mult @ ( mult @ ( mult @ SY50 @ sK4_X0 ) @ SY50 ) @ sK8_SY45 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(74,plain,
( ( ! [SY51: $i] :
( ( mult @ sK5_X3 @ ( mult @ SY51 @ ( mult @ sK9_SY47 @ SY51 ) ) )
= ( mult @ ( mult @ ( mult @ sK5_X3 @ SY51 ) @ sK9_SY47 ) @ SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(75,plain,
( ( ( mult @ ( mult @ sK10_SY49 @ sK2_X6 ) @ ( mult @ sK6_SY42 @ sK10_SY49 ) )
= ( mult @ ( mult @ sK10_SY49 @ ( mult @ sK2_X6 @ sK6_SY42 ) ) @ sK10_SY49 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(76,plain,
( ( ( mult @ sK11_SY50 @ ( mult @ sK4_X0 @ ( mult @ sK11_SY50 @ sK8_SY45 ) ) )
= ( mult @ ( mult @ ( mult @ sK11_SY50 @ sK4_X0 ) @ sK11_SY50 ) @ sK8_SY45 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(77,plain,
( ( ( mult @ sK5_X3 @ ( mult @ sK12_SY51 @ ( mult @ sK9_SY47 @ sK12_SY51 ) ) )
= ( mult @ ( mult @ ( mult @ sK5_X3 @ sK12_SY51 ) @ sK9_SY47 ) @ sK12_SY51 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(78,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[43,77,76,75,72,61,60,56,54,53,52,51,48,47,44]) ).
thf(79,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP748+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
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 10:49:00 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.31/4.81
% 27.31/4.81 No.of.Axioms: 11
% 27.31/4.81
% 27.31/4.81 Length.of.Defs: 0
% 27.31/4.81
% 27.31/4.81 Contains.Choice.Funs: false
% 27.31/4.81 ..
% 27.31/4.81
% 27.31/4.81 ********************************
% 27.31/4.81 * All subproblems solved! *
% 27.31/4.81 ********************************
% 27.31/4.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,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:78,loop_count:0,foatp_calls:1,translation:fof_full)
% 27.31/4.81
% 27.31/4.81 %**** Beginning of derivation protocol ****
% 27.31/4.81 % SZS output start CNFRefutation
% See solution above
% 27.31/4.81
% 27.31/4.81 %**** End of derivation protocol ****
% 27.31/4.81 %**** no. of clauses in derivation: 79 ****
% 27.31/4.81 %**** clause counter: 78 ****
% 27.31/4.81
% 27.31/4.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,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:78,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------