TSTP Solution File: LCL159-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL159-1 : 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 : n027.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 06:52:32 EDT 2023
% Result : Unsatisfiable 139.34s 139.38s
% Output : CNFRefutation 139.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 57 ( 47 unt; 10 typ; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 3 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
truth: $i ).
tff(decl_23,type,
implies: ( $i * $i ) > $i ).
tff(decl_24,type,
not: $i > $i ).
tff(decl_25,type,
or: ( $i * $i ) > $i ).
tff(decl_26,type,
and: ( $i * $i ) > $i ).
tff(decl_27,type,
xor: ( $i * $i ) > $i ).
tff(decl_28,type,
and_star: ( $i * $i ) > $i ).
tff(decl_29,type,
falsehood: $i ).
tff(decl_30,type,
x: $i ).
tff(decl_31,type,
y: $i ).
cnf(wajsberg_4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(or_commutativity,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
cnf(or_definition,axiom,
or(X1,X2) = implies(not(X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_definition) ).
cnf(wajsberg_2,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(and_definition,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',and_definition) ).
cnf(xor_definition,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(not(X1),X2)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',xor_commutativity) ).
cnf(c_0_10,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_11,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_12,axiom,
or(X1,X2) = or(X2,X1),
or_commutativity ).
cnf(c_0_13,axiom,
or(X1,X2) = implies(not(X1),X2),
or_definition ).
cnf(c_0_14,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_15,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_17,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_11]) ).
cnf(c_0_18,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_19,plain,
implies(implies(not(not(truth)),X1),X1) = truth,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
truth = implies(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_17]),c_0_11]) ).
cnf(c_0_21,plain,
implies(implies(X1,not(X2)),not(X2)) = implies(implies(not(X1),X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_22,plain,
not(not(truth)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11]) ).
cnf(c_0_23,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_21]),c_0_22]),c_0_22]) ).
cnf(c_0_24,plain,
implies(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_25,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_definition ).
cnf(c_0_26,plain,
implies(not(truth),X1) = truth,
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_27,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(not(X1),X2)),
xor_definition ).
cnf(c_0_28,plain,
and(X1,X2) = not(implies(not(not(X1)),not(X2))),
inference(rw,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_29,plain,
implies(X1,not(truth)) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_11]),c_0_22]),c_0_11]) ).
cnf(c_0_30,plain,
xor(X1,X2) = implies(not(not(implies(not(not(X1)),not(not(X2))))),not(implies(not(not(not(X1))),not(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_13]),c_0_28]),c_0_28]) ).
cnf(c_0_31,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_29]),c_0_22]),c_0_11]) ).
cnf(c_0_32,plain,
implies(implies(X1,X2),not(implies(not(X1),not(X2)))) = xor(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_33,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
prove_alternative_wajsberg_axiom ).
cnf(c_0_35,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity ).
cnf(c_0_36,plain,
implies(implies(X1,X2),not(implies(X2,X1))) = xor(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_16]),c_0_31]) ).
cnf(c_0_37,plain,
implies(implies(not(X1),X2),not(implies(X1,not(X2)))) = xor(not(X1),X2),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_38,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_39,plain,
implies(implies(X1,not(X2)),not(implies(not(X1),X2))) = xor(X1,not(X2)),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
xor(y,xor(truth,x)) != xor(x,xor(truth,y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_35]) ).
cnf(c_0_41,plain,
xor(truth,X1) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_11]),c_0_29]) ).
cnf(c_0_42,plain,
xor(not(X1),X2) = xor(not(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_16]),c_0_31]),c_0_36]) ).
cnf(c_0_43,plain,
xor(not(X1),X2) = xor(X1,not(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_44,negated_conjecture,
xor(y,not(x)) != xor(x,not(y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41]) ).
cnf(c_0_45,plain,
xor(X1,not(X2)) = xor(X2,not(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL159-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 17:18:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 139.34/139.38 % Version : CSE_E---1.5
% 139.34/139.38 % Problem : theBenchmark.p
% 139.34/139.38 % Proof found
% 139.34/139.38 % SZS status Theorem for theBenchmark.p
% 139.34/139.38 % SZS output start Proof
% See solution above
% 139.34/139.38 % Total time : 138.806000 s
% 139.34/139.38 % SZS output end Proof
% 139.34/139.38 % Total time : 138.815000 s
%------------------------------------------------------------------------------