%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL164-1 : TPTP v9.2.1. Released v1.0.0.
% 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 04:39:33 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 5 RR)
% Number of literals : 33 ( 32 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(implies_definition,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
cnf(axiom_2,axiom,
xor(X1,falsehood) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
cnf(axiom_4,axiom,
and_star(X1,truth) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
cnf(axiom_7,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
cnf(axiom_1,axiom,
not(X1) = xor(X1,truth),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_1) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(false_definition,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_definition) ).
cnf(and_star_commutativity,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(axiom_6,axiom,
and_star(xor(truth,X1),X1) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_6) ).
cnf(prove_wajsberg_axiom,negated_conjecture,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c_0_10,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
implies_definition ).
cnf(c_0_11,axiom,
xor(X1,falsehood) = X1,
axiom_2 ).
cnf(c_0_12,axiom,
and_star(X1,truth) = X1,
axiom_4 ).
cnf(c_0_13,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
axiom_7 ).
cnf(c_0_14,axiom,
not(X1) = xor(X1,truth),
axiom_1 ).
cnf(c_0_15,plain,
xor(truth,X1) = implies(X1,falsehood),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_16,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity ).
cnf(c_0_17,plain,
xor(X1,xor(truth,X2)) = xor(not(X1),X2),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
not(truth) = falsehood,
false_definition ).
cnf(c_0_19,plain,
implies(X1,falsehood) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14]) ).
cnf(c_0_20,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_18]),c_0_11]),c_0_14]) ).
cnf(c_0_21,plain,
not(and_star(X1,not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_15]),c_0_15]),c_0_19]),c_0_19]) ).
cnf(c_0_22,axiom,
and_star(X1,X2) = and_star(X2,X1),
and_star_commutativity ).
cnf(c_0_23,plain,
and_star(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
and_star(not(X1),X2) = not(implies(X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
and_star(X1,X2) = not(implies(X1,not(X2))),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_26,axiom,
and_star(xor(truth,X1),X1) = falsehood,
axiom_6 ).
cnf(c_0_27,plain,
not(implies(not(X1),not(X2))) = not(implies(X2,X1)),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(rw,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
prove_wajsberg_axiom ).
cnf(c_0_30,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_20]) ).
cnf(c_0_31,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_28]),c_0_11]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL164-1 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.14/0.31 % Computer : n029.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 22:04:59 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.373s
%------------------------------------------------------------------------------