%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET825-2 : TPTP v9.2.1. Released v3.2.0.
% 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 : n010.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 05:08:34 PM UTC 2026
% Result : Unsatisfiable 1.23s 1.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 8 unt; 5 nHn; 15 RR)
% Number of literals : 30 ( 6 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X1),v_xa(X1),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Relation_OIdI_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
cnf(cls_Relation_Opair__in__Id__conv__iff1_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X1)),c_Suc(v_xa(X1)),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_1,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X1),v_xa(X1),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
cls_conjecture_2 ).
cnf(c_0_7,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
cls_Relation_OIdI_0 ).
cnf(c_0_8,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
cls_Relation_Opair__in__Id__conv__iff1_0 ).
cnf(c_0_9,negated_conjecture,
( c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( v_xa(c_Relation_OId) = v_x(c_Relation_OId)
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X1)),c_Suc(v_xa(X1)),tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X1,tc_prod(tc_nat,tc_nat)) ),
cls_conjecture_3 ).
cnf(c_0_12,negated_conjecture,
( v_xa(c_Relation_OId) = v_x(c_Relation_OId)
| v_m = v_n ),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
~ v_Q(v_m),
cls_conjecture_1 ).
cnf(c_0_14,negated_conjecture,
v_m = v_n,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_7]),c_0_7])]),c_0_8]) ).
cnf(c_0_15,negated_conjecture,
v_Q(v_n),
cls_conjecture_0 ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET825-2 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.32 % Computer : n010.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % 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 02:36:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.23/1.71 % SZS output start CNFRefutation
% See solution above
% 1.23/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------