%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PUZ062-2 : TPTP v9.2.1. Released v3.2.0.
% 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 : n003.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 05:02:50 PM UTC 2026
% Result : Unsatisfiable 1.14s 1.84s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 40 ( 24 unt; 5 nHn; 32 RR)
% Number of literals : 61 ( 15 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 48 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Finite__Set_Ocard__insert__disjoint_0,axiom,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_insert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
cnf(cls_Finite__Set_Ofinite__Int_1,axiom,
( c_in(c_inter(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
cnf(cls_Mutil_Otiling__domino__finite_0,axiom,
( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X1,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Set_OInt__iff_1,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
cnf(cls_conjecture_4,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_5,negated_conjecture,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Set_OInt__iff_2,axiom,
( c_in(X1,c_inter(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
cnf(cls_conjecture_2,negated_conjecture,
c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Set_Oempty__iff_0,axiom,
~ c_in(X1,c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
cnf(cls_Set_Oinsert__iff_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
cnf(cls_conjecture_3,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(c_0_13,axiom,
( c_in(X3,X1,X2)
| c_Finite__Set_Ocard(c_insert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
cls_Finite__Set_Ocard__insert__disjoint_0 ).
cnf(c_0_14,axiom,
( c_in(c_inter(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
cls_Finite__Set_Ofinite__Int_1 ).
cnf(c_0_15,axiom,
( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X1,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
cls_Mutil_Otiling__domino__finite_0 ).
cnf(c_0_16,negated_conjecture,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
cls_conjecture_0 ).
cnf(c_0_17,plain,
( c_Finite__Set_Ocard(c_insert(X1,c_inter(X2,X3,X4),X4),X4) = c_Suc(c_Finite__Set_Ocard(c_inter(X2,X3,X4),X4))
| c_in(X1,c_inter(X2,X3,X4),X4)
| ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
cls_Set_OInt__iff_1 ).
cnf(c_0_20,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
cls_conjecture_4 ).
cnf(c_0_21,negated_conjecture,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
cls_conjecture_5 ).
cnf(c_0_22,negated_conjecture,
( c_Finite__Set_Ocard(c_insert(X1,c_inter(X2,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X2,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
| c_in(X1,c_inter(X2,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
cls_conjecture_1 ).
cnf(c_0_24,axiom,
( c_in(X1,c_inter(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
cls_Set_OInt__iff_2 ).
cnf(c_0_25,negated_conjecture,
c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
cls_conjecture_2 ).
cnf(c_0_26,axiom,
~ c_in(X1,c_emptyset,X2),
cls_Set_Oempty__iff_0 ).
cnf(c_0_27,negated_conjecture,
( c_in(X1,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(X1,c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_Oinsert__iff_1 ).
cnf(c_0_29,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
cls_conjecture_3 ).
cnf(c_0_30,negated_conjecture,
( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( ~ c_in(X1,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(X1,v_t,tc_prod(tc_nat,tc_nat)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_35,negated_conjecture,
~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : PUZ062-2 : TPTP v9.2.1. Released v3.2.0.
% 0.03/0.21 % 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
% 0.13/0.42 % Computer : n003.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8042.1875MB
% 0.13/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Tue May 5 01:35:11 EDT 2026
% 0.13/0.43 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 1.14/1.84 % Version : CSE_E---1.7
% 1.14/1.84 % Problem : theBenchmark.p
% 1.14/1.84 % SZS status Unsatisfiable for theBenchmark.p
% 1.14/1.84 % SZS output start CNFRefutation
% See solution above
% 1.14/1.84 % Total time : 1.380s
%------------------------------------------------------------------------------