TSTP Solution File: LCL146-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL146-1 : 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 : n021.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 06:52:29 EDT 2023
% Result : Unsatisfiable 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 45 ( 37 unt; 8 typ; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 51 ( 5 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/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
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(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(big_hat_definition,axiom,
big_hat(X1,X2) = not(big_V(not(X1),not(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',big_hat_definition) ).
cnf(big_V_definition,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
cnf(c_0_7,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_8,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_9,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_10,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_12,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_10]),c_0_8]) ).
cnf(c_0_13,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
implies(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_15,plain,
implies(X1,implies(X2,X1)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_14]),c_0_8]),c_0_8]) ).
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_9,c_0_15]),c_0_8]) ).
cnf(c_0_17,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_18,plain,
implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_19,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(spm,[status(thm)],[c_0_17,c_0_8]) ).
cnf(c_0_20,plain,
implies(implies(implies(X1,X2),X3),implies(X2,X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_15]),c_0_8]) ).
cnf(c_0_21,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_8]) ).
cnf(c_0_22,plain,
implies(not(truth),X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_8]) ).
cnf(c_0_23,plain,
implies(implies(not(X1),not(implies(X2,X1))),implies(implies(X1,X2),X2)) = truth,
inference(spm,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_24,plain,
not(not(truth)) = truth,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
implies(not(implies(X1,not(truth))),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_8]),c_0_22]),c_0_8]) ).
cnf(c_0_26,plain,
implies(X1,implies(not(X1),not(truth))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_8]) ).
cnf(c_0_27,axiom,
big_hat(X1,X2) = not(big_V(not(X1),not(X2))),
big_hat_definition ).
cnf(c_0_28,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
big_V_definition ).
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_9,c_0_26]),c_0_8]),c_0_19]),c_0_8]) ).
cnf(c_0_30,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
prove_wajsberg_theorem ).
cnf(c_0_31,plain,
big_hat(X1,X2) = not(implies(implies(not(X1),not(X2)),not(X2))),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
implies(implies(X1,not(truth)),not(truth)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_22]),c_0_8]) ).
cnf(c_0_33,plain,
implies(X1,not(truth)) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_29]),c_0_22]),c_0_8]) ).
cnf(c_0_34,negated_conjecture,
not(not(implies(implies(not(x),not(y)),not(y)))) != implies(implies(not(x),not(y)),not(y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_28]),c_0_31]) ).
cnf(c_0_35,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL146-1 : 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
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Fri Aug 25 01:09:55 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.011000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.014000 s
%------------------------------------------------------------------------------