TSTP Solution File: LCL109-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL109-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 : Thu Aug 31 06:52:18 EDT 2023
% Result : Unsatisfiable 208.10s 208.67s
% Output : CNFRefutation 208.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 56 ( 48 unt; 8 typ; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% 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 : 70 ( 5 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
not: $i > $i ).
tff(decl_23,type,
truth: $i ).
tff(decl_24,type,
xor: ( $i * $i ) > $i ).
tff(decl_25,type,
falsehood: $i ).
tff(decl_26,type,
and_star: ( $i * $i ) > $i ).
tff(decl_27,type,
implies: ( $i * $i ) > $i ).
tff(decl_28,type,
a: $i ).
tff(decl_29,type,
b: $i ).
cnf(axiom_6,axiom,
and_star(xor(truth,X1),X1) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_6) ).
cnf(and_star_commutativity,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(axiom_5,axiom,
and_star(X1,falsehood) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_5) ).
cnf(and_star_associativity,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_associativity) ).
cnf(axiom_8,axiom,
and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_8) ).
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_3,axiom,
xor(X1,X1) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_3) ).
cnf(axiom_2,axiom,
xor(X1,falsehood) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
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_4,axiom,
and_star(X1,truth) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
cnf(c_0_12,axiom,
and_star(xor(truth,X1),X1) = falsehood,
axiom_6 ).
cnf(c_0_13,axiom,
and_star(X1,X2) = and_star(X2,X1),
and_star_commutativity ).
cnf(c_0_14,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity ).
cnf(c_0_16,axiom,
and_star(X1,falsehood) = falsehood,
axiom_5 ).
cnf(c_0_17,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
and_star_associativity ).
cnf(c_0_18,plain,
and_star(X1,xor(X1,truth)) = falsehood,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
and_star(falsehood,X1) = falsehood,
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_20,axiom,
and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
axiom_8 ).
cnf(c_0_21,plain,
and_star(X1,and_star(xor(X1,truth),X2)) = falsehood,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
axiom_7 ).
cnf(c_0_23,axiom,
xor(X1,X1) = falsehood,
axiom_3 ).
cnf(c_0_24,axiom,
xor(X1,falsehood) = X1,
axiom_2 ).
cnf(c_0_25,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
prove_wajsberg_mv_4 ).
cnf(c_0_26,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
implies_definition ).
cnf(c_0_27,plain,
and_star(X1,xor(truth,and_star(xor(truth,X2),X1))) = and_star(X2,xor(truth,and_star(xor(truth,X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_15]),c_0_13]),c_0_15]),c_0_13]) ).
cnf(c_0_28,plain,
and_star(X1,and_star(X2,xor(X1,truth))) = falsehood,
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_29,plain,
xor(xor(truth,X1),X2) = xor(X1,xor(truth,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_30,axiom,
and_star(X1,truth) = X1,
axiom_4 ).
cnf(c_0_31,plain,
xor(truth,xor(truth,X1)) = xor(falsehood,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,plain,
xor(falsehood,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_33,negated_conjecture,
xor(truth,and_star(xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_34,plain,
and_star(X1,and_star(X2,X3)) = and_star(X2,and_star(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_17]) ).
cnf(c_0_35,plain,
and_star(X1,xor(truth,and_star(X1,xor(truth,and_star(X2,X1))))) = and_star(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_23]),c_0_24]),c_0_13]),c_0_29]),c_0_23]),c_0_24]),c_0_24]),c_0_30]) ).
cnf(c_0_36,plain,
xor(truth,xor(truth,X1)) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,xor(truth,xor(truth,and_star(b,xor(truth,a))))))))))) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_13]),c_0_27]),c_0_13]),c_0_17]),c_0_17]) ).
cnf(c_0_38,plain,
and_star(X1,and_star(X2,xor(truth,and_star(X1,xor(truth,and_star(X3,X1)))))) = and_star(X2,and_star(X3,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
and_star(xor(truth,and_star(xor(truth,X1),xor(truth,X2))),xor(truth,and_star(X1,xor(truth,and_star(X2,X1))))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_27]),c_0_36]),c_0_17]),c_0_13]),c_0_14]),c_0_16]),c_0_24]),c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_40,negated_conjecture,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,xor(falsehood,and_star(b,xor(truth,a)))))))))) != truth,
inference(rw,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_41,plain,
and_star(X1,and_star(X2,xor(truth,and_star(xor(truth,X2),xor(truth,X1))))) = and_star(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_13]),c_0_17]) ).
cnf(c_0_42,plain,
xor(X1,xor(truth,X2)) = xor(X2,xor(truth,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_43,plain,
and_star(X1,and_star(X2,xor(truth,and_star(X1,X2)))) = falsehood,
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_44,negated_conjecture,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(b,xor(truth,a))))))))) != truth,
inference(spm,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_45,plain,
and_star(X1,and_star(xor(truth,X2),xor(truth,and_star(X2,xor(truth,X1))))) = and_star(xor(truth,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_23]),c_0_24]) ).
cnf(c_0_46,plain,
and_star(X1,and_star(X2,xor(truth,and_star(X2,X1)))) = falsehood,
inference(spm,[status(thm)],[c_0_34,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL109-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 04:23:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 start to proof: theBenchmark
% 208.10/208.67 % Version : CSE_E---1.5
% 208.10/208.67 % Problem : theBenchmark.p
% 208.10/208.67 % Proof found
% 208.10/208.67 % SZS status Theorem for theBenchmark.p
% 208.10/208.67 % SZS output start Proof
% See solution above
% 208.10/208.68 % Total time : 207.459000 s
% 208.10/208.68 % SZS output end Proof
% 208.10/208.68 % Total time : 207.471000 s
%------------------------------------------------------------------------------