%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT023-1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n018.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 05:05:51 PM UTC 2026
% Result : Unsatisfiable 2.28s 2.03s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 36 ( 16 unt; 6 nHn; 29 RR)
% Number of literals : 64 ( 6 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-5 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 66 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_in(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_mem__def_1,axiom,
( c_in(X1,X2,X3)
| ~ hBOOL(hAPP(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_trans__def_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).
cnf(cls_conjecture_3,negated_conjecture,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_irrefl__def_1,axiom,
( c_Relation_Oirrefl(X1,X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
cnf(cls_irrefl__def_0,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Oirrefl(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
cnf(cls_conjecture_8,negated_conjecture,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
cnf(cls_in__rel__def_1,axiom,
( c_FunDef_Oin__rel(X1,X2,X3,X4,X5)
| ~ c_in(c_Pair(X2,X3,X4,X5),X1,tc_prod(X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_in__rel__def_0,axiom,
( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_FunDef_Oin__rel(X5,X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
cnf(c_0_13,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_in(X2,X1,X3) ),
cls_mem__def_0 ).
cnf(c_0_14,negated_conjecture,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_conjecture_2 ).
cnf(c_0_15,axiom,
( c_in(X1,X2,X3)
| ~ hBOOL(hAPP(X2,X1)) ),
cls_mem__def_1 ).
cnf(c_0_16,negated_conjecture,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X4,X3) ),
cls_trans__def_0 ).
cnf(c_0_18,negated_conjecture,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_3 ).
cnf(c_0_20,negated_conjecture,
~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_conjecture_4 ).
cnf(c_0_21,axiom,
( c_Relation_Oirrefl(X1,X2)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
cls_irrefl__def_1 ).
cnf(c_0_22,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Oirrefl(X3,X2) ),
cls_irrefl__def_0 ).
cnf(c_0_23,negated_conjecture,
( c_in(c_Pair(X1,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_24,negated_conjecture,
c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_conjecture_8 ).
cnf(c_0_27,axiom,
( c_FunDef_Oin__rel(X1,X2,X3,X4,X5)
| ~ c_in(c_Pair(X2,X3,X4,X5),X1,tc_prod(X4,X5)) ),
cls_in__rel__def_1 ).
cnf(c_0_28,negated_conjecture,
( v_b = v_a
| ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1 ),
cls_conjecture_6 ).
cnf(c_0_30,negated_conjecture,
~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_conjecture_5 ).
cnf(c_0_31,negated_conjecture,
c_FunDef_Oin__rel(v_F(v_P),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_32,negated_conjecture,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_33,axiom,
( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_FunDef_Oin__rel(X5,X1,X2,X3,X4) ),
cls_in__rel__def_0 ).
cnf(c_0_34,negated_conjecture,
c_FunDef_Oin__rel(v_F(v_P),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT023-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n018.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 : Tue May 5 01:53:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.28/2.03 % Version : CSE_E---1.7
% 2.28/2.03 % Problem : theBenchmark.p
% 2.28/2.03 % SZS status Unsatisfiable for theBenchmark.p
% 2.28/2.03 % SZS output start CNFRefutation
% See solution above
% 2.28/2.03 % Total time : 1.424s
%------------------------------------------------------------------------------