%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT004-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:08:10 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.80s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 40 ( 10 unt; 7 nHn; 29 RR)
% Number of literals : 112 ( 18 equ; 62 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 51 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_8,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
cnf(cls_conjecture_0,negated_conjecture,
( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_13,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_13) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(X2,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_15,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_15) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_insert__absorb_0,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_conjecture_17,negated_conjecture,
( X4 = X3
| hBOOL(c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| hBOOL(c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_17) ).
cnf(c_0_9,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_8]) ).
cnf(c_0_10,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_x != v_xa
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
c_0_9 ).
cnf(c_0_11,negated_conjecture,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_12,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_13]) ).
cnf(c_0_13,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(X2,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_3]) ).
cnf(c_0_14,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_xa != v_x
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cn,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
c_0_11 ).
cnf(c_0_16,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_15]) ).
cnf(c_0_17,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_1]) ).
cnf(c_0_18,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
c_0_12 ).
cnf(c_0_19,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(X2,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
c_0_13 ).
cnf(c_0_20,negated_conjecture,
( v_xa != v_x
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_21,negated_conjecture,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
c_0_16 ).
cnf(c_0_22,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
c_0_17 ).
cnf(c_0_23,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
cls_insert__code_1 ).
cnf(c_0_24,plain,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[cls_insert__absorb_0]) ).
cnf(c_0_25,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cn,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( X4 = X3
| hBOOL(c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| hBOOL(c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
cls_conjecture_17 ).
cnf(c_0_27,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| v_xa != v_x ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cn,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X4)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) = X2 ),
c_0_24 ).
cnf(c_0_31,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_15])]) ).
cnf(c_0_32,negated_conjecture,
( hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2 ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
v_xa != v_x,
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_34,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_15])]) ).
cnf(c_0_35,plain,
( ~ hBOOL(c_in(X1,X2,X4))
| hBOOL(c_in(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
~ hBOOL(c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_38,c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT004-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.39 % Computer : n004.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Mon Sep 21 04:25:41 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.80 % Version: 3.5.1
% 0.15/5.80 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.15/5.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.80 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.15/5.80 % Starting new_bool_3 with 600s (2) cores
% 0.15/5.80 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.80 % Starting sh5l with 300s (1) cores
% 0.15/5.80 % new_bool_3 with pid 2241077 completed with status 0
% 0.15/5.80 % Result found by new_bool_3
% 0.15/5.80 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.15/5.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.80 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.15/5.80 % Starting new_bool_3 with 600s (2) cores
% 0.15/5.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.80 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.80 % Search class: FGHSM-FSLS32-DFFFFFNN
% 0.15/5.80 % Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.15/5.80 % Starting SubtermCWHack with 61s (1) cores
% 0.15/5.80 % Starting SAT001_MinMin_p005000_rr_RG with 200s (1) cores
% 0.15/5.80 % SAT001_MinMin_p005000_rr_RG with pid 2241081 completed with status 0
% 0.15/5.80 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.15/5.80 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.15/5.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.80 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.15/5.80 % Starting new_bool_3 with 600s (2) cores
% 0.15/5.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.80 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.80 % Search class: FGHSM-FSLS32-DFFFFFNN
% 0.15/5.80 % Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.15/5.80 % Starting SubtermCWHack with 61s (1) cores
% 0.15/5.80 % Starting SAT001_MinMin_p005000_rr_RG with 200s (1) cores
% 0.15/5.80 % Preprocessing time : 0.007 s
% 0.15/5.80 % Presaturation interreduction done
% 0.15/5.80
% 0.15/5.80 % Proof found!
% 0.15/5.80 % SZS status Unsatisfiable
% 0.15/5.80 % SZS output start CNFRefutation
% See solution above
% 0.15/5.80 % Parsed axioms : 697
% 0.15/5.80 % Removed by relevancy pruning/SinE : 304
% 0.15/5.80 % Initial clauses : 393
% 0.15/5.80 % Removed in clause preprocessing : 4
% 0.15/5.80 % Initial clauses in saturation : 389
% 0.15/5.80 % Processed clauses : 3082
% 0.15/5.80 % ...of these trivial : 78
% 0.15/5.80 % ...subsumed : 1758
% 0.15/5.80 % ...remaining for further processing : 1246
% 0.15/5.80 % Other redundant clauses eliminated : 62
% 0.15/5.80 % Clauses deleted for lack of memory : 0
% 0.15/5.80 % Backward-subsumed : 123
% 0.15/5.80 % Backward-rewritten : 25
% 0.15/5.80 % Generated clauses : 10765
% 0.15/5.80 % ...of the previous two non-redundant : 9050
% 0.15/5.80 % ...aggressively subsumed : 0
% 0.15/5.80 % Contextual simplify-reflections : 2
% 0.15/5.80 % Paramodulations : 10683
% 0.15/5.80 % Factorizations : 14
% 0.15/5.80 % NegExts : 0
% 0.15/5.80 % Equation resolutions : 68
% 0.15/5.80 % Disequality decompositions : 0
% 0.15/5.80 % Total rewrite steps : 3513
% 0.15/5.80 % ...of those cached : 2237
% 0.15/5.80 % Propositional unsat checks : 0
% 0.15/5.80 % Propositional check models : 0
% 0.15/5.80 % Propositional check unsatisfiable : 0
% 0.15/5.80 % Propositional clauses : 0
% 0.15/5.80 % Propositional clauses after purity: 0
% 0.15/5.80 % Propositional unsat core size : 0
% 0.15/5.80 % Propositional preprocessing time : 0.000
% 0.15/5.80 % Propositional encoding time : 0.000
% 0.15/5.80 % Propositional solver time : 0.000
% 0.15/5.80 % Success case prop preproc time : 0.000
% 0.15/5.80 % Success case prop encoding time : 0.000
% 0.15/5.80 % Success case prop solver time : 0.000
% 0.15/5.80 % Current number of processed clauses : 779
% 0.15/5.80 % Positive orientable unit clauses : 186
% 0.15/5.80 % Positive unorientable unit clauses: 8
% 0.15/5.80 % Negative unit clauses : 167
% 0.15/5.80 % Non-unit-clauses : 418
% 0.15/5.80 % Current number of unprocessed clauses: 6568
% 0.15/5.80 % ...number of literals in the above : 14906
% 0.15/5.80 % Current number of archived formulas : 0
% 0.15/5.80 % Current number of archived clauses : 467
% 0.15/5.80 % Clause-clause subsumption calls (NU) : 41500
% 0.15/5.80 % Rec. Clause-clause subsumption calls : 36065
% 0.15/5.80 % Non-unit clause-clause subsumptions : 547
% 0.15/5.80 % Unit Clause-clause subsumption calls : 11590
% 0.15/5.80 % Rewrite failures with RHS unbound : 0
% 0.15/5.80 % BW rewrite match attempts : 871
% 0.15/5.80 % BW rewrite match successes : 240
% 0.15/5.80 % Condensation attempts : 0
% 0.15/5.80 % Condensation successes : 0
% 0.15/5.80 % Termbank termtop insertions : 190710
% 0.15/5.80 % Search garbage collected termcells : 2305
% 0.15/5.80
% 0.15/5.80 % -------------------------------------------------
% 0.15/5.80 % User time : 0.312 s
% 0.15/5.80 % System time : 0.013 s
% 0.15/5.80 % Total time : 0.324 s
% 0.15/5.80 % Maximum resident set size: 4744 pages
% 0.15/5.80
% 0.15/5.80 % -------------------------------------------------
% 0.15/5.80 % User time : 0.635 s
% 0.15/5.80 % System time : 0.031 s
% 0.15/5.80 % Total time : 0.666 s
% 0.15/5.80 % Maximum resident set size: 5376 pages
% 0.15/5.80 % E exiting
%------------------------------------------------------------------------------