TSTP Solution File: LCL109-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL109-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 2.43s 2.50s
% Output : CNFRefutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 55 unt; 8 typ; 0 def)
% Number of atoms : 55 ( 54 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 : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 10 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,
big_V: ( $i * $i ) > $i ).
tff(decl_26,type,
big_hat: ( $i * $i ) > $i ).
tff(decl_27,type,
ordered: ( $i * $i ) > $o ).
tff(decl_28,type,
x: $i ).
tff(decl_29,type,
y: $i ).
cnf(wajsberg_2,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(prove_mv_4,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_4) ).
cnf(big_V_definition,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).
cnf(c_0_6,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_7,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_8,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_9,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_10,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_11,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_9]),c_0_7]) ).
cnf(c_0_12,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
implies(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_14,plain,
implies(X1,implies(X2,X1)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_13]),c_0_7]),c_0_7]) ).
cnf(c_0_15,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_16,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_7]) ).
cnf(c_0_17,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_18,plain,
implies(implies(implies(X1,X2),X3),implies(X2,X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_14]),c_0_7]) ).
cnf(c_0_19,plain,
implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_20,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_7]) ).
cnf(c_0_21,plain,
implies(not(truth),X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_7]) ).
cnf(c_0_22,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11]),c_0_7]) ).
cnf(c_0_23,plain,
implies(implies(X1,not(truth)),not(truth)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_21]),c_0_7]) ).
cnf(c_0_24,plain,
not(not(truth)) = truth,
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_25,plain,
implies(not(implies(X1,not(truth))),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_23]),c_0_24]),c_0_7]) ).
cnf(c_0_26,plain,
implies(X1,implies(not(X1),not(truth))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_25]),c_0_7]) ).
cnf(c_0_27,plain,
implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_6]),c_0_7]) ).
cnf(c_0_28,plain,
implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_7]) ).
cnf(c_0_29,plain,
implies(not(X1),not(truth)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_26]),c_0_7]),c_0_17]),c_0_7]) ).
cnf(c_0_30,plain,
implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_7]) ).
cnf(c_0_31,plain,
implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,X1)),implies(X3,X1)) = implies(implies(X1,X2),implies(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_7]) ).
cnf(c_0_32,plain,
implies(X1,not(truth)) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_29]),c_0_21]),c_0_7]) ).
cnf(c_0_33,plain,
implies(implies(implies(X1,implies(X2,X3)),X3),implies(implies(X3,X2),X2)) = truth,
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_34,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_30]),c_0_7]),c_0_30]),c_0_7]) ).
cnf(c_0_35,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_15]),c_0_7]),c_0_32]) ).
cnf(c_0_36,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_32]),c_0_32]) ).
cnf(c_0_37,plain,
implies(implies(X1,X2),implies(implies(implies(X3,implies(X2,X1)),X1),X2)) = truth,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
implies(X1,implies(implies(implies(X2,X1),X3),X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_9]),c_0_7]) ).
cnf(c_0_39,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
implies(implies(implies(X1,implies(X2,X3)),X3),X2) = implies(X3,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_37]),c_0_7]),c_0_34]),c_0_38]),c_0_7]) ).
cnf(c_0_41,plain,
implies(implies(implies(X1,X2),X2),implies(X3,X1)) = implies(X3,implies(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_42,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
implies(X1,not(implies(X1,X2))) = implies(X2,not(implies(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_35]),c_0_35]),c_0_39]),c_0_39]) ).
cnf(c_0_44,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth,
prove_mv_4 ).
cnf(c_0_45,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
big_V_definition ).
cnf(c_0_46,plain,
implies(implies(implies(X1,implies(X2,X3)),X3),X1) = implies(X3,X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X3),X2)),
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_48,plain,
implies(implies(X1,X2),not(implies(implies(X2,X1),X1))) = not(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_19]),c_0_9]),c_0_32]),c_0_39]) ).
cnf(c_0_49,negated_conjecture,
implies(implies(implies(x,y),implies(y,x)),implies(y,x)) != truth,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
implies(implies(implies(X1,implies(implies(X2,X3),X3)),X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_8]) ).
cnf(c_0_51,plain,
implies(implies(X1,X2),implies(implies(implies(X2,X1),X1),X3)) = implies(X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_36]),c_0_35]) ).
cnf(c_0_52,negated_conjecture,
implies(y,implies(implies(y,implies(implies(x,y),x)),x)) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_34]),c_0_34]) ).
cnf(c_0_53,plain,
implies(X1,implies(implies(X2,X1),X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_11]),c_0_7]),c_0_34]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL109-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 06:51:36 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.64 start to proof: theBenchmark
% 2.43/2.50 % Version : CSE_E---1.5
% 2.43/2.50 % Problem : theBenchmark.p
% 2.43/2.50 % Proof found
% 2.43/2.50 % SZS status Theorem for theBenchmark.p
% 2.43/2.50 % SZS output start Proof
% See solution above
% 4.29/2.51 % Total time : 1.848000 s
% 4.29/2.51 % SZS output end Proof
% 4.29/2.51 % Total time : 1.851000 s
%------------------------------------------------------------------------------