%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL152-1 : 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 : n011.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 04:39:31 PM UTC 2026
% Result : Unsatisfiable 4.40s 3.33s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 11 RR)
% Number of literals : 49 ( 48 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 72 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
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,
implies(big_hat(x,y),z) != implies(implies(x,y),implies(x,z)),
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,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_10,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_11,plain,
implies(X1,implies(implies(X2,X1),X1)) = truth,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_8]) ).
cnf(c_0_13,plain,
implies(X1,truth) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),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_7,c_0_13]),c_0_8]),c_0_8]) ).
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_10,c_0_14]),c_0_8]) ).
cnf(c_0_17,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_18,plain,
implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_19,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_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_14]),c_0_8]) ).
cnf(c_0_21,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12]),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_17]),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_15,c_0_10]) ).
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_15,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_10,c_0_26]),c_0_8]),c_0_17]),c_0_8]) ).
cnf(c_0_30,negated_conjecture,
implies(big_hat(x,y),z) != implies(implies(x,y),implies(x,z)),
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(X1,not(truth)) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_29]),c_0_22]),c_0_8]) ).
cnf(c_0_33,negated_conjecture,
implies(not(implies(implies(not(x),not(y)),not(y))),z) != implies(implies(x,y),implies(x,z)),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
implies(implies(X1,X2),implies(not(X2),not(X1))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_32]),c_0_32]) ).
cnf(c_0_35,plain,
implies(implies(X1,not(truth)),not(truth)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_22]),c_0_8]) ).
cnf(c_0_36,negated_conjecture,
implies(not(implies(implies(not(y),not(x)),not(x))),z) != implies(implies(x,y),implies(x,z)),
inference(rw,[status(thm)],[c_0_33,c_0_10]) ).
cnf(c_0_37,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_34]),c_0_8]),c_0_15]),c_0_8]) ).
cnf(c_0_38,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_32]),c_0_32]) ).
cnf(c_0_39,negated_conjecture,
implies(not(implies(implies(x,y),not(x))),z) != implies(implies(x,y),implies(x,z)),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,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_7,c_0_7]),c_0_8]) ).
cnf(c_0_42,plain,
implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_9]),c_0_8]) ).
cnf(c_0_43,negated_conjecture,
implies(not(z),implies(implies(x,y),not(x))) != implies(implies(x,y),implies(x,z)),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_8]) ).
cnf(c_0_46,negated_conjecture,
implies(not(z),implies(x,not(implies(x,y)))) != implies(implies(x,y),implies(x,z)),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,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_10,c_0_45]),c_0_8]),c_0_45]),c_0_8]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_37]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL152-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 22:04:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.40/3.33 % Version : CSE_E---1.7
% 4.40/3.33 % Problem : theBenchmark.p
% 4.40/3.33 % SZS status Unsatisfiable for theBenchmark.p
% 4.40/3.33 % SZS output start CNFRefutation
% See solution above
% 4.40/3.35 % Total time : 2.371s
%------------------------------------------------------------------------------