%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL276-3 : TPTP v9.2.1. Released v2.3.0.
% 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 : n029.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 04:39:57 PM UTC 2026
% Result : Unsatisfiable 12.97s 8.49s
% Output : CNFRefutation 13.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 66 ( 37 unt; 0 nHn; 25 RR)
% Number of literals : 106 ( 7 equ; 47 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 128 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_5,axiom,
axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).
cnf(implies_definition,axiom,
implies(X1,X2) = or(not(X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',implies_definition) ).
cnf(rule_2,axiom,
( theorem(X1)
| ~ theorem(implies(X2,X1))
| ~ theorem(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_2) ).
cnf(rule_1,axiom,
( theorem(X1)
| ~ axiom(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(X1,X2),or(X2,X1))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).
cnf(axiom_1_3,axiom,
axiom(implies(X1,or(X2,X1))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
cnf(axiom_1_2,axiom,
axiom(implies(or(X1,X1),X1)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
cnf(equivalent_defn,axiom,
equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).
cnf(and_defn,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-1.ax',and_defn) ).
cnf(prove_this,negated_conjecture,
~ theorem(equivalent(or(r,or(p,q)),or(p,or(q,r)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
cnf(c_0_11,axiom,
axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
axiom_1_5 ).
cnf(c_0_12,axiom,
implies(X1,X2) = or(not(X1),X2),
implies_definition ).
cnf(c_0_13,axiom,
( theorem(X1)
| ~ theorem(implies(X2,X1))
| ~ theorem(X2) ),
rule_2 ).
cnf(c_0_14,axiom,
( theorem(X1)
| ~ axiom(X1) ),
rule_1 ).
cnf(c_0_15,plain,
axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,axiom,
axiom(implies(or(X1,X2),or(X2,X1))),
axiom_1_4 ).
cnf(c_0_17,axiom,
axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
axiom_1_6 ).
cnf(c_0_18,axiom,
axiom(implies(X1,or(X2,X1))),
axiom_1_3 ).
cnf(c_0_19,plain,
( theorem(X1)
| ~ theorem(X2)
| ~ theorem(or(not(X2),X1)) ),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_20,plain,
theorem(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
axiom(or(not(or(X1,X2)),or(X2,X1))),
inference(rw,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_22,plain,
axiom(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_23,axiom,
axiom(implies(or(X1,X1),X1)),
axiom_1_2 ).
cnf(c_0_24,plain,
axiom(or(not(X1),or(X2,X1))),
inference(rw,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_25,plain,
( theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X2,or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
theorem(or(not(or(X1,X2)),or(X2,X1))),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_27,plain,
theorem(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2)))),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_28,plain,
axiom(or(not(or(X1,X1)),X1)),
inference(rw,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_29,plain,
theorem(or(not(X1),or(X2,X1))),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_30,plain,
theorem(or(X1,or(not(or(X2,X1)),X2))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( theorem(or(not(or(X1,X2)),or(X1,X3)))
| ~ theorem(or(not(X2),X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_32,plain,
( theorem(or(X1,X2))
| ~ theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_33,plain,
theorem(or(not(or(X1,X1)),X1)),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_34,plain,
( theorem(or(X1,X2))
| ~ theorem(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_35,plain,
( theorem(or(not(or(X1,not(X2))),X1))
| ~ theorem(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_36,plain,
( theorem(or(X1,X2))
| ~ theorem(or(not(X3),X2))
| ~ theorem(or(X1,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_37,plain,
theorem(or(X1,not(or(X1,X1)))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X1,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_39,plain,
( theorem(X1)
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
cnf(c_0_40,plain,
( theorem(or(X1,not(or(not(X2),not(X2)))))
| ~ theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
( theorem(or(X1,X2))
| ~ theorem(or(not(X3),X2))
| ~ theorem(X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_38]) ).
cnf(c_0_42,plain,
( theorem(X1)
| ~ theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_43,plain,
theorem(or(X1,or(not(X2),X2))),
inference(spm,[status(thm)],[c_0_25,c_0_29]) ).
cnf(c_0_44,axiom,
equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
equivalent_defn ).
cnf(c_0_45,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_defn ).
cnf(c_0_46,plain,
( theorem(X1)
| ~ theorem(or(not(X2),not(X2)))
| ~ theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
( theorem(or(X1,not(or(not(X2),not(X2)))))
| ~ theorem(X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_48,plain,
theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
~ theorem(equivalent(or(r,or(p,q)),or(p,or(q,r)))),
prove_this ).
cnf(c_0_50,plain,
equivalent(X1,X2) = not(or(not(or(not(X1),X2)),not(or(not(X2),X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_12]),c_0_12]),c_0_45]) ).
cnf(c_0_51,plain,
( theorem(X1)
| ~ theorem(or(X1,or(not(X2),not(X2))))
| ~ theorem(X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
~ theorem(not(or(not(or(not(or(r,or(p,q))),or(p,or(q,r)))),not(or(not(or(p,or(q,r))),or(r,or(p,q))))))),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
( theorem(not(or(not(X1),X2)))
| ~ theorem(or(not(X2),not(X1)))
| ~ theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_31]) ).
cnf(c_0_55,plain,
( theorem(or(X1,not(not(X2))))
| ~ theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( ~ theorem(or(not(not(or(not(or(p,or(q,r))),or(r,or(p,q))))),not(or(not(or(r,or(p,q))),or(p,or(q,r))))))
| ~ theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( theorem(or(not(not(X1)),X2))
| ~ theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_55]) ).
cnf(c_0_58,plain,
( theorem(or(X1,or(X2,X3)))
| ~ theorem(or(not(X4),X3))
| ~ theorem(or(X2,X4)) ),
inference(spm,[status(thm)],[c_0_41,c_0_31]) ).
cnf(c_0_59,negated_conjecture,
( ~ theorem(or(not(or(not(or(r,or(p,q))),or(p,or(q,r)))),or(not(or(p,or(q,r))),or(r,or(p,q)))))
| ~ theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
( theorem(or(X1,or(X2,or(X3,or(X4,X5)))))
| ~ theorem(or(X2,or(X4,or(X3,X5)))) ),
inference(spm,[status(thm)],[c_0_58,c_0_20]) ).
cnf(c_0_61,negated_conjecture,
( ~ theorem(or(not(or(r,or(p,q))),or(p,or(q,r))))
| ~ theorem(or(not(or(p,or(q,r))),or(p,or(r,q)))) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,plain,
( theorem(or(X1,or(X2,X3)))
| ~ theorem(or(X1,or(X2,X4)))
| ~ theorem(or(not(X4),X3)) ),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_63,negated_conjecture,
~ theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_26])]) ).
cnf(c_0_64,plain,
( theorem(or(not(or(X1,or(X2,X3))),or(X2,X4)))
| ~ theorem(or(not(or(X1,X3)),X4)) ),
inference(spm,[status(thm)],[c_0_62,c_0_20]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL276-3 : TPTP v9.2.1. Released v2.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n029.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 22:19:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 12.97/8.49 % Version : CSE_E---1.7
% 12.97/8.49 % Problem : theBenchmark.p
% 12.97/8.49 % SZS status Unsatisfiable for theBenchmark.p
% 12.97/8.49 % SZS output start CNFRefutation
% See solution above
% 13.07/8.53 % Total time : 6.382s
%------------------------------------------------------------------------------