%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG178+1 : TPTP v9.2.1. Released v2.7.0.
% 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 : n022.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 04:07:45 PM UTC 2026
% Result : Theorem 1.54s 1.84s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 93 ( 26 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 106 ( 37 ~; 30 |; 15 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax3,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> op1(X1,op1(X1,X2)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(ax2,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(ax4,axiom,
~ ! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> op2(X1,op2(X1,X2)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(c_0_4,negated_conjecture,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,negated_conjecture,
! [X33,X34,X35,X36,X37,X38,X39,X40] :
( ( ~ sorti1(X33)
| sorti2(h(X33)) )
& ( ~ sorti2(X34)
| sorti1(j(X34)) )
& ( ~ sorti1(X35)
| ~ sorti1(X36)
| h(op1(X35,X36)) = op2(h(X35),h(X36)) )
& ( ~ sorti2(X37)
| ~ sorti2(X38)
| j(op2(X37,X38)) = op1(j(X37),j(X38)) )
& ( ~ sorti2(X39)
| h(j(X39)) = X39 )
& ( ~ sorti1(X40)
| j(h(X40)) = X40 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X29,X30] :
( ~ sorti1(X29)
| ~ sorti1(X30)
| op1(X29,op1(X29,X30)) = X30 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])]) ).
cnf(c_0_7,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( op1(X1,op1(X1,X2)) = X2
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_12,plain,
! [X27,X28] :
( ~ sorti2(X27)
| ~ sorti2(X28)
| sorti2(op2(X27,X28)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])]) ).
cnf(c_0_13,negated_conjecture,
( h(op1(X1,j(X2))) = op2(h(X1),X2)
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( op1(j(X1),j(op2(X1,X2))) = j(X2)
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_9]),c_0_9]) ).
cnf(c_0_15,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
( sorti2(esk1_0)
& sorti2(esk2_0)
& op2(esk1_0,op2(esk1_0,esk2_0)) != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])]) ).
cnf(c_0_17,negated_conjecture,
( op2(h(j(X1)),op2(X1,X2)) = h(j(X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_9]),c_0_15]) ).
cnf(c_0_18,plain,
op2(esk1_0,op2(esk1_0,esk2_0)) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( op2(X1,op2(X1,X2)) = h(j(X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_8]) ).
cnf(c_0_20,plain,
sorti2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
sorti2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
h(j(esk2_0)) != esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_8]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG178+1 : TPTP v9.2.1. Released v2.7.0.
% 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 : n022.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 : Tue May 5 10:23:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.54/1.84 % Version : CSE_E---1.7
% 1.54/1.84 % Problem : theBenchmark.p
% 1.54/1.84 % SZS status Theorem for theBenchmark.p
% 1.54/1.84 % SZS output start CNFRefutation
% See solution above
% 1.54/1.85 % Total time : 1.418s
%------------------------------------------------------------------------------