%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HAL002+1 : TPTP v9.2.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : 300s
% DateTime : Tue May 5 04:28:26 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 10 unt; 0 def)
% Number of atoms : 227 ( 64 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 243 ( 91 ~; 114 |; 21 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 136 ( 6 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subtract_in_domain,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> element(subtract(X2,X5,X6),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
fof(subtract_to_0,axiom,
! [X2,X4] :
( element(X4,X2)
=> subtract(X2,X4,X4) = zero(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_to_0) ).
fof(properties_for_injection_2,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X4] :
( ( element(X4,X2)
& apply(X1,X4) = zero(X3) )
=> X4 = zero(X2) ) )
=> injection_2(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_injection_2) ).
fof(my,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',my) ).
fof(x_morphism,hypothesis,
morphism(x,any1,any2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_morphism) ).
fof(properties_for_injection,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2)
& apply(X1,X5) = apply(X1,X6) )
=> X5 = X6 ) )
=> injection(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_injection) ).
fof(subtract_distribution,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> apply(X1,subtract(X2,X5,X6)) = subtract(X3,apply(X1,X5),apply(X1,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
fof(morphism,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ( ! [X4] :
( element(X4,X2)
=> element(apply(X1,X4),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(subtract_cancellation,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> subtract(X2,X5,subtract(X2,X5,X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).
fof(injection_properties_2,axiom,
! [X1,X2,X3] :
( ( injection_2(X1)
& morphism(X1,X2,X3) )
=> ! [X4] :
( ( element(X4,X2)
& apply(X1,X4) = zero(X3) )
=> X4 = zero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injection_properties_2) ).
fof(injection_properties,axiom,
! [X1,X2,X3] :
( ( injection(X1)
& morphism(X1,X2,X3) )
=> ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2)
& apply(X1,X5) = apply(X1,X6) )
=> X5 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',injection_properties) ).
fof(c_0_11,plain,
! [X155,X156,X157] :
( ~ element(X156,X155)
| ~ element(X157,X155)
| element(subtract(X155,X156,X157),X155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_in_domain])]) ).
fof(c_0_12,plain,
! [X158,X159] :
( ~ element(X159,X158)
| subtract(X158,X159,X159) = zero(X158) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_to_0])]) ).
fof(c_0_13,plain,
! [X172,X173,X174] :
( ( element(esk9_3(X172,X173,X174),X173)
| ~ morphism(X172,X173,X174)
| injection_2(X172) )
& ( apply(X172,esk9_3(X172,X173,X174)) = zero(X174)
| ~ morphism(X172,X173,X174)
| injection_2(X172) )
& ( esk9_3(X172,X173,X174) != zero(X173)
| ~ morphism(X172,X173,X174)
| injection_2(X172) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[properties_for_injection_2])])])])])]) ).
fof(c_0_14,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(assume_negation,[status(cth)],[my]) ).
cnf(c_0_15,plain,
( element(subtract(X2,X1,X3),X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( subtract(X2,X1,X1) = zero(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( element(esk9_3(X1,X2,X3),X2)
| injection_2(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
morphism(x,any1,any2),
inference(split_conjunct,[status(thm)],[x_morphism]) ).
fof(c_0_19,plain,
! [X105,X106,X107] :
( ( element(esk1_2(X105,X106),X106)
| ~ morphism(X105,X106,X107)
| injection(X105) )
& ( element(esk2_2(X105,X106),X106)
| ~ morphism(X105,X106,X107)
| injection(X105) )
& ( apply(X105,esk1_2(X105,X106)) = apply(X105,esk2_2(X105,X106))
| ~ morphism(X105,X106,X107)
| injection(X105) )
& ( esk1_2(X105,X106) != esk2_2(X105,X106)
| ~ morphism(X105,X106,X107)
| injection(X105) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[properties_for_injection])])])])])]) ).
fof(c_0_20,negated_conjecture,
( ( ~ injection(x)
| ~ injection_2(x) )
& ( injection(x)
| injection_2(x) ) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( element(zero(X1),X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,hypothesis,
( injection_2(x)
| element(esk9_3(x,any1,any2),any1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,plain,
! [X163,X164,X165,X166,X167] :
( ~ morphism(X163,X164,X165)
| ~ element(X166,X164)
| ~ element(X167,X164)
| apply(X163,subtract(X164,X166,X167)) = subtract(X165,apply(X163,X166),apply(X163,X167)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_distribution])])]) ).
fof(c_0_24,plain,
! [X96,X97,X98,X99] :
( ( ~ element(X99,X97)
| element(apply(X96,X99),X98)
| ~ morphism(X96,X97,X98) )
& ( apply(X96,zero(X97)) = zero(X98)
| ~ morphism(X96,X97,X98) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[morphism])])])]) ).
cnf(c_0_25,plain,
( element(esk1_2(X1,X2),X2)
| injection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( ~ injection(x)
| ~ injection_2(x) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,hypothesis,
( injection_2(x)
| element(zero(any1),any1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5))
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2)
| ~ element(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( apply(X1,zero(X2)) = zero(X3)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,hypothesis,
( injection(x)
| element(esk1_2(x,any1),any1) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_31,negated_conjecture,
( element(zero(any1),any1)
| ~ injection(x) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_32,plain,
! [X160,X161,X162] :
( ~ element(X161,X160)
| ~ element(X162,X160)
| subtract(X160,X161,subtract(X160,X161,X162)) = X162 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_cancellation])]) ).
cnf(c_0_33,hypothesis,
( subtract(any2,apply(x,X1),apply(x,X2)) = apply(x,subtract(any1,X1,X2))
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_34,hypothesis,
apply(x,zero(any1)) = zero(any2),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_35,hypothesis,
element(zero(any1),any1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
( apply(X1,esk1_2(X1,X2)) = apply(X1,esk2_2(X1,X2))
| injection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,plain,
( element(esk2_2(X1,X2),X2)
| injection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_38,plain,
( element(apply(X3,X1),X4)
| ~ element(X1,X2)
| ~ morphism(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_39,plain,
! [X168,X169,X170,X171] :
( ~ injection_2(X168)
| ~ morphism(X168,X169,X170)
| ~ element(X171,X169)
| apply(X168,X171) != zero(X170)
| X171 = zero(X169) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[injection_properties_2])])]) ).
cnf(c_0_40,plain,
( subtract(X2,X1,subtract(X2,X1,X3)) = X3
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,hypothesis,
( subtract(any2,apply(x,X1),zero(any2)) = apply(x,subtract(any1,X1,zero(any1)))
| ~ element(X1,any1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_42,hypothesis,
( apply(x,esk2_2(x,any1)) = apply(x,esk1_2(x,any1))
| injection(x) ),
inference(spm,[status(thm)],[c_0_36,c_0_18]) ).
cnf(c_0_43,hypothesis,
( injection(x)
| element(esk2_2(x,any1),any1) ),
inference(spm,[status(thm)],[c_0_37,c_0_18]) ).
cnf(c_0_44,hypothesis,
( element(apply(x,X1),any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_45,plain,
( X4 = zero(X2)
| ~ injection_2(X1)
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2)
| apply(X1,X4) != zero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( subtract(X1,X2,zero(X1)) = X2
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_16]) ).
cnf(c_0_47,hypothesis,
( subtract(any2,apply(x,esk1_2(x,any1)),zero(any2)) = apply(x,subtract(any1,esk2_2(x,any1),zero(any1)))
| injection(x) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_48,hypothesis,
( injection(x)
| element(apply(x,esk1_2(x,any1)),any2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_43]) ).
cnf(c_0_49,hypothesis,
( X1 = zero(any1)
| apply(x,X1) != zero(any2)
| ~ injection_2(x)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_50,negated_conjecture,
( injection(x)
| injection_2(x) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_51,hypothesis,
( subtract(any2,apply(x,X1),apply(x,subtract(any1,X1,X2))) = apply(x,X2)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_33]),c_0_44]),c_0_44]) ).
cnf(c_0_52,hypothesis,
( apply(x,subtract(any1,esk2_2(x,any1),zero(any1))) = apply(x,esk1_2(x,any1))
| injection(x) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( X1 = zero(any1)
| injection(x)
| apply(x,X1) != zero(any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,hypothesis,
( subtract(any2,apply(x,esk2_2(x,any1)),apply(x,esk1_2(x,any1))) = zero(any2)
| injection(x) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]),c_0_35])]),c_0_43]) ).
cnf(c_0_55,negated_conjecture,
( subtract(any1,X1,X2) = zero(any1)
| injection(x)
| apply(x,subtract(any1,X1,X2)) != zero(any2)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[c_0_53,c_0_15]) ).
cnf(c_0_56,hypothesis,
( apply(x,subtract(any1,esk2_2(x,any1),esk1_2(x,any1))) = zero(any2)
| injection(x) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_54]),c_0_43]),c_0_30]) ).
fof(c_0_57,plain,
! [X100,X101,X102,X103,X104] :
( ~ injection(X100)
| ~ morphism(X100,X101,X102)
| ~ element(X103,X101)
| ~ element(X104,X101)
| apply(X100,X103) != apply(X100,X104)
| X103 = X104 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[injection_properties])])]) ).
cnf(c_0_58,negated_conjecture,
( subtract(any1,esk2_2(x,any1),esk1_2(x,any1)) = zero(any1)
| injection(x) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_43]),c_0_30]) ).
cnf(c_0_59,plain,
( injection(X1)
| esk1_2(X1,X2) != esk2_2(X1,X2)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_60,plain,
( X4 = X5
| ~ injection(X1)
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2)
| ~ element(X5,X2)
| apply(X1,X4) != apply(X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,negated_conjecture,
( subtract(any1,esk2_2(x,any1),zero(any1)) = esk1_2(x,any1)
| injection(x) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_58]),c_0_43]),c_0_30]) ).
cnf(c_0_62,hypothesis,
( injection(x)
| esk2_2(x,any1) != esk1_2(x,any1) ),
inference(spm,[status(thm)],[c_0_59,c_0_18]) ).
cnf(c_0_63,hypothesis,
( X1 = X2
| apply(x,X1) != apply(x,X2)
| ~ injection(x)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[c_0_60,c_0_18]) ).
cnf(c_0_64,negated_conjecture,
injection(x),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_61]),c_0_43]),c_0_62]) ).
cnf(c_0_65,plain,
( apply(X1,esk9_3(X1,X2,X3)) = zero(X3)
| injection_2(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_66,hypothesis,
( X1 = X2
| apply(x,X1) != apply(x,X2)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_67,hypothesis,
( apply(x,esk9_3(x,any1,any2)) = zero(any2)
| injection_2(x) ),
inference(spm,[status(thm)],[c_0_65,c_0_18]) ).
cnf(c_0_68,negated_conjecture,
~ injection_2(x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_64])]) ).
cnf(c_0_69,hypothesis,
( X1 = zero(any1)
| apply(x,X1) != zero(any2)
| ~ element(X1,any1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_34]),c_0_35])]) ).
cnf(c_0_70,hypothesis,
apply(x,esk9_3(x,any1,any2)) = zero(any2),
inference(sr,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,hypothesis,
element(esk9_3(x,any1,any2),any1),
inference(sr,[status(thm)],[c_0_22,c_0_68]) ).
cnf(c_0_72,plain,
( injection_2(X1)
| esk9_3(X1,X2,X3) != zero(X2)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_73,hypothesis,
esk9_3(x,any1,any2) = zero(any1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_74,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_18])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL002+1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 19:07:54 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.368s
%------------------------------------------------------------------------------