%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HAL006+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 : n029.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 04:28:27 PM UTC 2026
% Result : Theorem 13.61s 8.84s
% Output : CNFRefutation 13.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 100 ( 27 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 100 ( 38 ~; 35 |; 19 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 30 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lemma12,conjecture,
! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma12) ).
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(lemma8,axiom,
! [X19] :
( element(X19,e)
=> ? [X21,X22,X23] :
( element(X21,b)
& element(X22,e)
& subtract(e,apply(g,X21),X19) = X22
& element(X23,a)
& apply(gamma,apply(f,X23)) = X22
& apply(g,apply(alpha,X23)) = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma8) ).
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(alpha_morphism,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alpha_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(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
fof(c_0_7,negated_conjecture,
~ ! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
inference(assume_negation,[status(cth)],[lemma12]) ).
fof(c_0_8,plain,
! [X104,X105,X106,X107] :
( ( ~ element(X107,X105)
| element(apply(X104,X107),X106)
| ~ morphism(X104,X105,X106) )
& ( apply(X104,zero(X105)) = zero(X106)
| ~ morphism(X104,X105,X106) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[morphism])])])]) ).
fof(c_0_9,plain,
! [X179] :
( ( element(esk11_1(X179),b)
| ~ element(X179,e) )
& ( element(esk12_1(X179),e)
| ~ element(X179,e) )
& ( subtract(e,apply(g,esk11_1(X179)),X179) = esk12_1(X179)
| ~ element(X179,e) )
& ( element(esk13_1(X179),a)
| ~ element(X179,e) )
& ( apply(gamma,apply(f,esk13_1(X179))) = esk12_1(X179)
| ~ element(X179,e) )
& ( apply(g,apply(alpha,esk13_1(X179))) = esk12_1(X179)
| ~ element(X179,e) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lemma8])])])]) ).
fof(c_0_10,negated_conjecture,
! [X184,X185] :
( element(esk14_0,e)
& ( ~ element(X184,b)
| ~ element(X185,b)
| apply(g,subtract(b,X184,X185)) != esk14_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X171,X172,X173,X174,X175] :
( ~ morphism(X171,X172,X173)
| ~ element(X174,X172)
| ~ element(X175,X172)
| apply(X171,subtract(X172,X174,X175)) = subtract(X173,apply(X171,X174),apply(X171,X175)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_distribution])])]) ).
cnf(c_0_12,plain,
( element(apply(X3,X1),X4)
| ~ element(X1,X2)
| ~ morphism(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
morphism(alpha,a,b),
inference(split_conjunct,[status(thm)],[alpha_morphism]) ).
cnf(c_0_14,plain,
( element(esk13_1(X1),a)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
element(esk14_0,e),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X168,X169,X170] :
( ~ element(X169,X168)
| ~ element(X170,X168)
| subtract(X168,X169,subtract(X168,X169,X170)) = X170 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_cancellation])]) ).
cnf(c_0_17,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_18,plain,
( element(esk11_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,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_11]) ).
cnf(c_0_20,plain,
( element(apply(alpha,X1),b)
| ~ element(X1,a) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
element(esk13_1(esk14_0),a),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( apply(g,apply(alpha,esk13_1(X1))) = esk12_1(X1)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,plain,
( subtract(X2,X1,subtract(X2,X1,X3)) = X3
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( element(apply(g,X1),e)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
element(esk11_1(esk14_0),b),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_26,plain,
( subtract(e,apply(g,esk11_1(X1)),X1) = esk12_1(X1)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
( subtract(e,apply(g,X1),apply(g,X2)) = apply(g,subtract(b,X1,X2))
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
element(apply(alpha,esk13_1(esk14_0)),b),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
apply(g,apply(alpha,esk13_1(esk14_0))) = esk12_1(esk14_0),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
( subtract(e,X1,subtract(e,X1,esk14_0)) = esk14_0
| ~ element(X1,e) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
element(apply(g,esk11_1(esk14_0)),e),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
subtract(e,apply(g,esk11_1(esk14_0)),esk14_0) = esk12_1(esk14_0),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( apply(g,subtract(b,X1,apply(alpha,esk13_1(esk14_0)))) = subtract(e,apply(g,X1),esk12_1(esk14_0))
| ~ element(X1,b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
subtract(e,apply(g,esk11_1(esk14_0)),esk12_1(esk14_0)) = esk14_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( ~ element(X1,b)
| ~ element(X2,b)
| apply(g,subtract(b,X1,X2)) != esk14_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_36,negated_conjecture,
apply(g,subtract(b,esk11_1(esk14_0),apply(alpha,esk13_1(esk14_0)))) = esk14_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL006+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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 19:08:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 13.61/8.84 % Version : CSE_E---1.7
% 13.61/8.84 % Problem : theBenchmark.p
% 13.61/8.84 % SZS status Theorem for theBenchmark.p
% 13.61/8.84 % SZS output start CNFRefutation
% See solution above
% 13.71/8.90 % Total time : 6.390s
%------------------------------------------------------------------------------