%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HAL003+3 : TPTP v9.2.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 1.15s 1.95s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 57 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 60 ( 26 ~; 22 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(properties_for_surjection,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X7] :
( element(X7,X3)
=> ? [X8] :
( element(X8,X2)
& apply(X1,X8) = X7 ) ) )
=> surjection(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',properties_for_surjection) ).
fof(g_surjection,conjecture,
surjection(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_surjection) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
fof(lemma12,axiom,
! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma12) ).
fof(subtract_in_domain,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> element(subtract(X2,X5,X6),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
fof(c_0_5,plain,
! [X123,X124,X125,X127] :
( ( element(esk4_3(X123,X124,X125),X125)
| ~ morphism(X123,X124,X125)
| surjection(X123) )
& ( ~ element(X127,X124)
| apply(X123,X127) != esk4_3(X123,X124,X125)
| ~ morphism(X123,X124,X125)
| surjection(X123) ) ),
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_surjection])])])])])]) ).
fof(c_0_6,negated_conjecture,
~ surjection(g),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[g_surjection])]) ).
cnf(c_0_7,plain,
( surjection(X3)
| ~ element(X1,X2)
| apply(X3,X1) != esk4_3(X3,X2,X4)
| ~ morphism(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_9,negated_conjecture,
~ surjection(g),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X183] :
( ( element(esk14_1(X183),b)
| ~ element(X183,e) )
& ( element(esk15_1(X183),b)
| ~ element(X183,e) )
& ( apply(g,subtract(b,esk14_1(X183),esk15_1(X183))) = X183
| ~ element(X183,e) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lemma12])])])]) ).
cnf(c_0_11,plain,
( element(esk4_3(X1,X2,X3),X3)
| surjection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( apply(g,X1) != esk4_3(g,b,e)
| ~ element(X1,b) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_13,plain,
( apply(g,subtract(b,esk14_1(X1),esk15_1(X1))) = X1
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
element(esk4_3(g,b,e),e),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_9]) ).
fof(c_0_15,plain,
! [X163,X164,X165] :
( ~ element(X164,X163)
| ~ element(X165,X163)
| element(subtract(X163,X164,X165),X163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_in_domain])]) ).
cnf(c_0_16,plain,
~ element(subtract(b,esk14_1(esk4_3(g,b,e)),esk15_1(esk4_3(g,b,e))),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])]),c_0_14])]) ).
cnf(c_0_17,plain,
( element(subtract(X2,X1,X3),X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( ~ element(esk15_1(esk4_3(g,b,e)),b)
| ~ element(esk14_1(esk4_3(g,b,e)),b) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
( element(esk15_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
~ element(esk14_1(esk4_3(g,b,e)),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14])]) ).
cnf(c_0_21,plain,
( element(esk14_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.28 % Problem : HAL003+3 : TPTP v9.2.1. Released v2.6.0.
% 0.06/0.28 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.52 % Computer : n013.cluster.edu
% 0.12/0.52 % Model : x86_64 x86_64
% 0.12/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.52 % Memory : 8042.1875MB
% 0.12/0.52 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.52 % CPULimit : 300
% 0.12/0.52 % WCLimit : 300
% 0.12/0.52 % DateTime : Mon May 4 19:07:56 EDT 2026
% 0.12/0.54 % CPUTime :
% 0.14/0.56 % start to proof: theBenchmark
% 1.15/1.95 % Version : CSE_E---1.7
% 1.15/1.95 % Problem : theBenchmark.p
% 1.15/1.95 % SZS status Theorem for theBenchmark.p
% 1.15/1.95 % SZS output start CNFRefutation
% See solution above
% 1.15/1.96 % Total time : 1.390s
%------------------------------------------------------------------------------