%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL015+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 05:04:15 PM UTC 2026
% Result : Theorem 2.00s 1.93s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 3 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(goals,conjecture,
composition(top,top) = top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_9,plain,
! [X48,X49] : converse(composition(X48,X49)) = composition(converse(X49),converse(X48)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_10,plain,
! [X45] : converse(converse(X45)) = X45,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_11,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X41] : composition(X41,one) = X41,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_14,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X31,X32,X33] : join(X31,join(X32,X33)) = join(join(X31,X32),X33),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_17,plain,
! [X52] : top = join(X52,complement(X52)),
inference(variable_rename,[status(thm)],[def_top]) ).
fof(c_0_18,plain,
! [X50,X51] : join(composition(converse(X50),complement(composition(X50,X51))),complement(X51)) = complement(X51),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_19,plain,
! [X29,X30] : join(X29,X30) = join(X30,X29),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_20,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_12]) ).
cnf(c_0_21,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_26,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_29,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_30,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]),c_0_28]) ).
fof(c_0_31,plain,
! [X42,X43,X44] : composition(join(X42,X43),X44) = join(composition(X42,X44),composition(X43,X44)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_32,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_33,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_22]) ).
cnf(c_0_34,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_24]) ).
cnf(c_0_37,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
fof(c_0_38,negated_conjecture,
composition(top,top) != top,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
cnf(c_0_39,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
composition(top,top) != top,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_41,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL015+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n008.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:39:59 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 2.00/1.93 % Version : CSE_E---1.7
% 2.00/1.93 % Problem : theBenchmark.p
% 2.00/1.93 % SZS status Theorem for theBenchmark.p
% 2.00/1.93 % SZS output start CNFRefutation
% See solution above
% 2.00/1.94 % Total time : 1.368s
%------------------------------------------------------------------------------