TSTP Solution File: GRP002-10 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP002-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:15:18 EDT 2022
% Result : Unsatisfiable 17.82s 18.06s
% Output : CNFRefutation 17.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 33
% Syntax : Number of formulae : 110 ( 96 unt; 14 typ; 0 def)
% Number of atoms : 248 ( 164 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 839 ( 6 ~; 0 |; 0 &; 833 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 11 con; 0-4 aty)
% Number of variables : 218 ( 0 ^ 218 !; 0 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_d,type,
d: $i ).
thf(tp_h,type,
h: $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_ifeq,type,
ifeq: $i > $i > $i > $i > $i ).
thf(tp_ifeq2,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_j,type,
j: $i ).
thf(tp_k,type,
k: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $i ).
thf(tp_true,type,
true: $i ).
thf(1,axiom,
! [Y: $i,Z: $i,V: $i,X: $i,W: $i,U: $i] :
( ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ V @ W ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ U @ Z @ W ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(2,axiom,
! [U: $i,Z: $i,W: $i,Y: $i,V: $i,X: $i] :
( ( ifeq @ ( product @ U @ Z @ W ) @ true @ ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ X @ V @ W ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(3,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ( ifeq2 @ ( product @ X @ Y @ W ) @ true @ ( ifeq2 @ ( product @ X @ Y @ Z ) @ true @ Z @ W ) @ W )
= W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
thf(5,axiom,
! [X: $i] :
( ( product @ X @ ( inverse @ X ) @ identity )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(6,axiom,
! [X: $i] :
( ( product @ ( inverse @ X ) @ X @ identity )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(7,axiom,
! [X: $i] :
( ( product @ X @ identity @ X )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(8,axiom,
! [X: $i] :
( ( product @ identity @ X @ X )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ Y @ X @ identity ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity_2) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ X @ Y @ identity ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity_1) ).
thf(13,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(14,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,negated_conjecture,
( product @ k @ ( inverse @ b ) @ identity )
!= true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
thf(16,negated_conjecture,
( ( product @ j @ ( inverse @ h ) @ k )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
thf(17,negated_conjecture,
( ( product @ h @ b @ j )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_b_is_j) ).
thf(18,negated_conjecture,
( ( product @ d @ ( inverse @ b ) @ h )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
thf(19,negated_conjecture,
( ( product @ c @ ( inverse @ a ) @ d )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
thf(20,negated_conjecture,
( ( product @ a @ b @ c )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(21,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(22,plain,
( ( ! [Y: $i,Z: $i,V: $i,X: $i,W: $i,U: $i] :
( ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ V @ W ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ U @ Z @ W ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,plain,
( ( ! [U: $i,Z: $i,W: $i,Y: $i,V: $i,X: $i] :
( ( ifeq @ ( product @ U @ Z @ W ) @ true @ ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ X @ V @ W ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ( ifeq2 @ ( product @ X @ Y @ W ) @ true @ ( ifeq2 @ ( product @ X @ Y @ Z ) @ true @ Z @ W ) @ W )
= W ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( product @ X @ ( inverse @ X ) @ identity )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( product @ ( inverse @ X ) @ X @ identity )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( product @ X @ identity @ X )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( product @ identity @ X @ X )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(30,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ Y @ X @ identity ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ X @ Y @ identity ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(34,plain,
( ( ( ( product @ k @ ( inverse @ b ) @ identity )
!= true ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(35,plain,
( ( ( product @ j @ ( inverse @ h ) @ k )
= true )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(36,plain,
( ( ( product @ h @ b @ j )
= true )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(37,plain,
( ( ( product @ d @ ( inverse @ b ) @ h )
= true )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(38,plain,
( ( ( product @ c @ ( inverse @ a ) @ d )
= true )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(39,plain,
( ( ( product @ a @ b @ c )
= true )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(40,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(41,plain,
( ( ( ( product @ k @ ( inverse @ b ) @ identity )
!= true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(42,plain,
( ( ( product @ a @ b @ c )
= true )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(43,plain,
( ( ( product @ c @ ( inverse @ a ) @ d )
= true )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(44,plain,
( ( ( product @ d @ ( inverse @ b ) @ h )
= true )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(45,plain,
( ( ( product @ h @ b @ j )
= true )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(46,plain,
( ( ( product @ j @ ( inverse @ h ) @ k )
= true )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(47,plain,
( ( ( ( product @ k @ ( inverse @ b ) @ identity )
!= true ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ X @ Y @ identity ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i] :
( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ Y @ X @ identity ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(50,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(51,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(52,plain,
( ( ! [X: $i] :
( ( product @ identity @ X @ X )
= true ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(53,plain,
( ( ! [X: $i] :
( ( product @ X @ identity @ X )
= true ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( product @ ( inverse @ X ) @ X @ identity )
= true ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(55,plain,
( ( ! [X: $i] :
( ( product @ X @ ( inverse @ X ) @ identity )
= true ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ( ifeq2 @ ( product @ X @ Y @ W ) @ true @ ( ifeq2 @ ( product @ X @ Y @ Z ) @ true @ Z @ W ) @ W )
= W ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(58,plain,
( ( ! [U: $i,Z: $i,W: $i,Y: $i,V: $i,X: $i] :
( ( ifeq @ ( product @ U @ Z @ W ) @ true @ ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ X @ V @ W ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(59,plain,
( ( ! [Y: $i,Z: $i,V: $i,X: $i,W: $i,U: $i] :
( ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ V @ W ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ U @ Z @ W ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(60,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(61,plain,
( ( ( product @ k @ ( inverse @ b ) @ identity )
= true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(62,plain,
! [SV1: $i] :
( ( ! [SY32: $i] :
( ( ifeq @ ( product @ SV1 @ SV1 @ SY32 ) @ true @ ( product @ SV1 @ SY32 @ identity ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(63,plain,
! [SV2: $i] :
( ( ! [SY33: $i] :
( ( ifeq @ ( product @ SV2 @ SV2 @ SY33 ) @ true @ ( product @ SY33 @ SV2 @ identity ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(64,plain,
! [SV3: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ( ifeq2 @ SV3 @ SV3 @ SY34 @ SY35 )
= SY34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(65,plain,
! [SV4: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( ifeq @ SV4 @ SV4 @ SY36 @ SY37 )
= SY36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(66,plain,
! [SV5: $i] :
( ( ( product @ identity @ SV5 @ SV5 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(67,plain,
! [SV6: $i] :
( ( ( product @ SV6 @ identity @ SV6 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(68,plain,
! [SV7: $i] :
( ( ( product @ ( inverse @ SV7 ) @ SV7 @ identity )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(69,plain,
! [SV8: $i] :
( ( ( product @ SV8 @ ( inverse @ SV8 ) @ identity )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(70,plain,
! [SV9: $i] :
( ( ! [SY38: $i] :
( ( product @ SV9 @ SY38 @ ( multiply @ SV9 @ SY38 ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(71,plain,
! [SV10: $i] :
( ( ! [SY39: $i,SY40: $i,SY41: $i] :
( ( ifeq2 @ ( product @ SV10 @ SY39 @ SY40 ) @ true @ ( ifeq2 @ ( product @ SV10 @ SY39 @ SY41 ) @ true @ SY41 @ SY40 ) @ SY40 )
= SY40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(72,plain,
! [SV11: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i,SY45: $i,SY46: $i] :
( ( ifeq @ ( product @ SV11 @ SY42 @ SY43 ) @ true @ ( ifeq @ ( product @ SY44 @ SY42 @ SY45 ) @ true @ ( ifeq @ ( product @ SY46 @ SY44 @ SV11 ) @ true @ ( product @ SY46 @ SY45 @ SY43 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(73,plain,
! [SV12: $i] :
( ( ! [SY47: $i,SY48: $i,SY49: $i,SY50: $i,SY51: $i] :
( ( ifeq @ ( product @ SV12 @ SY47 @ SY48 ) @ true @ ( ifeq @ ( product @ SY49 @ SY48 @ SY50 ) @ true @ ( ifeq @ ( product @ SY49 @ SV12 @ SY51 ) @ true @ ( product @ SY51 @ SY47 @ SY50 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(74,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(75,plain,
! [SV13: $i,SV1: $i] :
( ( ( ifeq @ ( product @ SV1 @ SV1 @ SV13 ) @ true @ ( product @ SV1 @ SV13 @ identity ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(76,plain,
! [SV14: $i,SV2: $i] :
( ( ( ifeq @ ( product @ SV2 @ SV2 @ SV14 ) @ true @ ( product @ SV14 @ SV2 @ identity ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(77,plain,
! [SV15: $i,SV3: $i] :
( ( ! [SY52: $i] :
( ( ifeq2 @ SV3 @ SV3 @ SV15 @ SY52 )
= SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(78,plain,
! [SV16: $i,SV4: $i] :
( ( ! [SY53: $i] :
( ( ifeq @ SV4 @ SV4 @ SV16 @ SY53 )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(79,plain,
! [SV17: $i,SV9: $i] :
( ( ( product @ SV9 @ SV17 @ ( multiply @ SV9 @ SV17 ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV18: $i,SV10: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ( ifeq2 @ ( product @ SV10 @ SV18 @ SY54 ) @ true @ ( ifeq2 @ ( product @ SV10 @ SV18 @ SY55 ) @ true @ SY55 @ SY54 ) @ SY54 )
= SY54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV19: $i,SV11: $i] :
( ( ! [SY56: $i,SY57: $i,SY58: $i,SY59: $i] :
( ( ifeq @ ( product @ SV11 @ SV19 @ SY56 ) @ true @ ( ifeq @ ( product @ SY57 @ SV19 @ SY58 ) @ true @ ( ifeq @ ( product @ SY59 @ SY57 @ SV11 ) @ true @ ( product @ SY59 @ SY58 @ SY56 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV20: $i,SV12: $i] :
( ( ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( ifeq @ ( product @ SV12 @ SV20 @ SY60 ) @ true @ ( ifeq @ ( product @ SY61 @ SY60 @ SY62 ) @ true @ ( ifeq @ ( product @ SY61 @ SV12 @ SY63 ) @ true @ ( product @ SY63 @ SV20 @ SY62 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV21: $i,SV15: $i,SV3: $i] :
( ( ( ifeq2 @ SV3 @ SV3 @ SV15 @ SV21 )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV22: $i,SV16: $i,SV4: $i] :
( ( ( ifeq @ SV4 @ SV4 @ SV16 @ SV22 )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV23: $i,SV18: $i,SV10: $i] :
( ( ! [SY64: $i] :
( ( ifeq2 @ ( product @ SV10 @ SV18 @ SV23 ) @ true @ ( ifeq2 @ ( product @ SV10 @ SV18 @ SY64 ) @ true @ SY64 @ SV23 ) @ SV23 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV24: $i,SV19: $i,SV11: $i] :
( ( ! [SY65: $i,SY66: $i,SY67: $i] :
( ( ifeq @ ( product @ SV11 @ SV19 @ SV24 ) @ true @ ( ifeq @ ( product @ SY65 @ SV19 @ SY66 ) @ true @ ( ifeq @ ( product @ SY67 @ SY65 @ SV11 ) @ true @ ( product @ SY67 @ SY66 @ SV24 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV25: $i,SV20: $i,SV12: $i] :
( ( ! [SY68: $i,SY69: $i,SY70: $i] :
( ( ifeq @ ( product @ SV12 @ SV20 @ SV25 ) @ true @ ( ifeq @ ( product @ SY68 @ SV25 @ SY69 ) @ true @ ( ifeq @ ( product @ SY68 @ SV12 @ SY70 ) @ true @ ( product @ SY70 @ SV20 @ SY69 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV26: $i,SV23: $i,SV18: $i,SV10: $i] :
( ( ( ifeq2 @ ( product @ SV10 @ SV18 @ SV23 ) @ true @ ( ifeq2 @ ( product @ SV10 @ SV18 @ SV26 ) @ true @ SV26 @ SV23 ) @ SV23 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV27: $i,SV24: $i,SV19: $i,SV11: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ( ifeq @ ( product @ SV11 @ SV19 @ SV24 ) @ true @ ( ifeq @ ( product @ SV27 @ SV19 @ SY71 ) @ true @ ( ifeq @ ( product @ SY72 @ SV27 @ SV11 ) @ true @ ( product @ SY72 @ SY71 @ SV24 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV28: $i,SV25: $i,SV20: $i,SV12: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ( ifeq @ ( product @ SV12 @ SV20 @ SV25 ) @ true @ ( ifeq @ ( product @ SV28 @ SV25 @ SY73 ) @ true @ ( ifeq @ ( product @ SV28 @ SV12 @ SY74 ) @ true @ ( product @ SY74 @ SV20 @ SY73 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV29: $i,SV27: $i,SV24: $i,SV19: $i,SV11: $i] :
( ( ! [SY75: $i] :
( ( ifeq @ ( product @ SV11 @ SV19 @ SV24 ) @ true @ ( ifeq @ ( product @ SV27 @ SV19 @ SV29 ) @ true @ ( ifeq @ ( product @ SY75 @ SV27 @ SV11 ) @ true @ ( product @ SY75 @ SV29 @ SV24 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV30: $i,SV28: $i,SV25: $i,SV20: $i,SV12: $i] :
( ( ! [SY76: $i] :
( ( ifeq @ ( product @ SV12 @ SV20 @ SV25 ) @ true @ ( ifeq @ ( product @ SV28 @ SV25 @ SV30 ) @ true @ ( ifeq @ ( product @ SV28 @ SV12 @ SY76 ) @ true @ ( product @ SY76 @ SV20 @ SV30 ) @ true ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV31: $i,SV29: $i,SV27: $i,SV24: $i,SV19: $i,SV11: $i] :
( ( ( ifeq @ ( product @ SV11 @ SV19 @ SV24 ) @ true @ ( ifeq @ ( product @ SV27 @ SV19 @ SV29 ) @ true @ ( ifeq @ ( product @ SV31 @ SV27 @ SV11 ) @ true @ ( product @ SV31 @ SV29 @ SV24 ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV32: $i,SV30: $i,SV28: $i,SV25: $i,SV20: $i,SV12: $i] :
( ( ( ifeq @ ( product @ SV12 @ SV20 @ SV25 ) @ true @ ( ifeq @ ( product @ SV28 @ SV25 @ SV30 ) @ true @ ( ifeq @ ( product @ SV28 @ SV12 @ SV32 ) @ true @ ( product @ SV32 @ SV20 @ SV30 ) @ true ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(95,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,94,93,88,84,83,79,76,75,74,69,68,67,66,61,46,45,44,43]) ).
thf(96,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP002-10 : TPTP v8.1.0. Released v7.3.0.
% 0.13/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 17:19:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 18
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.38 (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:20,loop_count:0,foatp_calls:0,translation:fof_full).....
% 17.82/18.06
% 17.82/18.06 ********************************
% 17.82/18.06 * All subproblems solved! *
% 17.82/18.06 ********************************
% 17.82/18.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:95,loop_count:0,foatp_calls:1,translation:fof_full)
% 17.82/18.06
% 17.82/18.06 %**** Beginning of derivation protocol ****
% 17.82/18.06 % SZS output start CNFRefutation
% See solution above
% 17.82/18.06
% 17.82/18.06 %**** End of derivation protocol ****
% 17.82/18.06 %**** no. of clauses in derivation: 96 ****
% 17.82/18.06 %**** clause counter: 95 ****
% 17.82/18.06
% 17.82/18.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:95,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------