%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL121-1 : 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 : n012.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 04:12:28 PM UTC 2026
% Result : Unsatisfiable 167.98s 130.10s
% Output : CNFRefutation 168.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 13 unt; 0 nHn; 30 RR)
% Number of literals : 57 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Comb_Odiamond__strip__lemmaE_1,axiom,
( c_in(c_Pair(X5,c_Comb_Odiamond__strip__lemmaE__1(X1,X5,X4,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_Comb_Odiamond(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Comb_Odiamond(v_r,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_in(c_Pair(v_ya,v_x(X1),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Comb_Odiamond__strip__lemmaE_0,axiom,
( c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X1,X5,X4,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Comb_Odiamond(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_0) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_in(c_Pair(X1,v_x(X1),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_Transitive__Closure_Ortrancl__trans_0,axiom,
( c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
cnf(cls_Transitive__Closure_Or__into__rtrancl_0,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Transitive__Closure_Or__into__rtrancl_0) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ c_in(c_Pair(v_xaa,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(c_0_10,axiom,
( c_in(c_Pair(X5,c_Comb_Odiamond__strip__lemmaE__1(X1,X5,X4,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_Comb_Odiamond(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
cls_Comb_Odiamond__strip__lemmaE_1 ).
cnf(c_0_11,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
cls_conjecture_2 ).
cnf(c_0_12,negated_conjecture,
c_Comb_Odiamond(v_r,t_a),
cls_conjecture_0 ).
cnf(c_0_13,negated_conjecture,
( c_in(c_Pair(v_ya,v_x(X1),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
cls_conjecture_4 ).
cnf(c_0_14,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
cls_conjecture_3 ).
cnf(c_0_15,axiom,
( c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X1,X5,X4,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Comb_Odiamond(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
cls_Comb_Odiamond__strip__lemmaE_0 ).
cnf(c_0_16,negated_conjecture,
( c_in(c_Pair(X1,v_x(X1),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
cls_conjecture_5 ).
cnf(c_0_17,negated_conjecture,
( c_in(c_Pair(X1,c_Comb_Odiamond__strip__lemmaE__1(v_r,X1,v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_18,negated_conjecture,
c_in(c_Pair(v_ya,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,X1,v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_11]),c_0_12])]) ).
cnf(c_0_20,axiom,
( c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_Transitive__Closure_Ortrancl__trans_0 ).
cnf(c_0_21,negated_conjecture,
c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_22,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
cls_Transitive__Closure_Or__into__rtrancl_0 ).
cnf(c_0_23,negated_conjecture,
c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( ~ c_in(c_Pair(v_xaa,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
cls_conjecture_6 ).
cnf(c_0_25,negated_conjecture,
c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( c_in(c_Pair(v_xaa,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : COL121-1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.06 % 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
% 0.06/0.25 % Computer : n012.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon May 4 16:18:01 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 167.98/130.10 % Version : CSE_E---1.7
% 167.98/130.10 % Problem : theBenchmark.p
% 167.98/130.10 % SZS status Unsatisfiable for theBenchmark.p
% 167.98/130.10 % SZS output start CNFRefutation
% See solution above
% 168.37/130.42 % Total time : 117.185s
%------------------------------------------------------------------------------