%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE084-10 : TPTP v9.2.1. Released v7.5.0.
% 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 : 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 : Tue May 5 04:35:40 PM UTC 2026
% Result : Unsatisfiable 3.65s 3.17s
% Output : CNFRefutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 6 RR)
% Number of literals : 52 ( 51 equ; 3 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 : 82 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity,axiom,
addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
cnf(additive_commutativity,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(multiplicative_associativity,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
cnf(domain1,axiom,
multiplication(antidomain(X1),X1) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
cnf(left_annihilation,axiom,
multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
cnf(left_distributivity,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
cnf(domain3,axiom,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
cnf(right_distributivity,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
cnf(multiplicative_left_identity,axiom,
multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(multiplicative_right_identity,axiom,
multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(domain2,axiom,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
cnf(additive_associativity,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
cnf(additive_idempotence,axiom,
addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
cnf(goals,negated_conjecture,
domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(domain4,axiom,
domain(X1) = antidomain(antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
cnf(c_0_15,axiom,
addition(X1,zero) = X1,
additive_identity ).
cnf(c_0_16,axiom,
addition(X1,X2) = addition(X2,X1),
additive_commutativity ).
cnf(c_0_17,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
multiplicative_associativity ).
cnf(c_0_18,axiom,
multiplication(antidomain(X1),X1) = zero,
domain1 ).
cnf(c_0_19,axiom,
multiplication(zero,X1) = zero,
left_annihilation ).
cnf(c_0_20,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
left_distributivity ).
cnf(c_0_21,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,axiom,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
domain3 ).
cnf(c_0_23,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
right_distributivity ).
cnf(c_0_24,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_25,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_21]) ).
cnf(c_0_26,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_27,axiom,
multiplication(one,X1) = X1,
multiplicative_left_identity ).
cnf(c_0_28,axiom,
multiplication(X1,one) = X1,
multiplicative_right_identity ).
cnf(c_0_29,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_18]),c_0_15]) ).
cnf(c_0_30,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_15]) ).
cnf(c_0_31,axiom,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
domain2 ).
cnf(c_0_32,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,multiplication(X2,X3))) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_33,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_34,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_35,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,addition(X3,X2))) = multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,X3)),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_36,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_18]) ).
cnf(c_0_37,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),multiplication(X1,X2)) = zero,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_34]),c_0_21]) ).
cnf(c_0_39,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
additive_associativity ).
cnf(c_0_40,axiom,
addition(X1,X1) = X1,
additive_idempotence ).
cnf(c_0_41,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),multiplication(X1,antidomain(X2))) = multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_26]),c_0_28]) ).
cnf(c_0_42,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),antidomain(antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_27]) ).
cnf(c_0_43,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
goals ).
cnf(c_0_45,axiom,
domain(X1) = antidomain(antidomain(X1)),
domain4 ).
cnf(c_0_46,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_16]) ).
cnf(c_0_47,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38]),c_0_27]),c_0_38]),c_0_27]) ).
cnf(c_0_48,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_26]),c_0_16]) ).
cnf(c_0_49,negated_conjecture,
antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) != antidomain(antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_50,plain,
antidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_31]),c_0_16]),c_0_48]),c_0_27]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE084-10 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.13 % 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
% 0.16/0.34 % Computer : n027.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 : Mon May 4 20:29:05 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.65/3.17 % Version : CSE_E---1.7
% 3.65/3.17 % Problem : theBenchmark.p
% 3.65/3.17 % SZS status Unsatisfiable for theBenchmark.p
% 3.65/3.17 % SZS output start CNFRefutation
% See solution above
% 3.65/3.18 % Total time : 2.370s
%------------------------------------------------------------------------------