%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO031-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n031.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 04:11:21 PM UTC 2026
% Result : Unsatisfiable 4.44s 3.63s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of clauses : 97 ( 97 unt; 0 nHn; 7 RR)
% Number of literals : 97 ( 96 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 202 ( 42 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(property3,axiom,
multiply(add(X1,inverse(X1)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property3) ).
cnf(additive_inverse,axiom,
add(X1,inverse(X1)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
cnf(multiplicative_inverse,axiom,
multiply(X1,inverse(X1)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).
cnf(l2,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
cnf(property3_dual,axiom,
add(multiply(X1,inverse(X1)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property3_dual) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
cnf(l1,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(l3,axiom,
add(add(multiply(X1,X2),multiply(X2,X3)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
cnf(l4,axiom,
multiply(multiply(add(X1,X2),add(X2,X3)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
cnf(distributivity,axiom,
add(multiply(X1,X2),add(multiply(X2,X3),multiply(X3,X1))) = multiply(add(X1,X2),multiply(add(X2,X3),add(X3,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).
cnf(prove_multiply_add_property,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add_property) ).
cnf(c_0_12,axiom,
multiply(add(X1,inverse(X1)),X2) = X2,
property3 ).
cnf(c_0_13,axiom,
add(X1,inverse(X1)) = n1,
additive_inverse ).
cnf(c_0_14,plain,
multiply(n1,X1) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
multiply(X1,inverse(X1)) = n0,
multiplicative_inverse ).
cnf(c_0_16,plain,
inverse(n1) = n0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
l2 ).
cnf(c_0_18,plain,
add(n1,n0) = n1,
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_19,axiom,
add(multiply(X1,inverse(X1)),X2) = X2,
property3_dual ).
cnf(c_0_20,plain,
add(X1,n1) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14]) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_22,plain,
add(n0,X1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_23,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
l1 ).
cnf(c_0_24,plain,
multiply(X1,n1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_20]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(n0,X2),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_26,plain,
multiply(n0,add(X1,X2)) = n0,
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_27,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
multiply(n0,inverse(inverse(X1))) = multiply(X1,n0),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_29,plain,
multiply(n0,X1) = n0,
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_30,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_31,plain,
add(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_32,axiom,
add(add(multiply(X1,X2),multiply(X2,X3)),X2) = X2,
l3 ).
cnf(c_0_33,axiom,
multiply(multiply(add(X1,X2),add(X2,X3)),X2) = X2,
l4 ).
cnf(c_0_34,plain,
multiply(X1,n0) = n0,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
multiply(X1,add(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_36,plain,
add(X1,add(X1,X2)) = add(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
add(multiply(X1,X2),add(multiply(X2,X3),X2)) = X2,
inference(rw,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_38,plain,
multiply(add(X1,X2),multiply(add(X2,X3),X2)) = X2,
inference(rw,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_39,plain,
add(X1,n0) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_34]) ).
cnf(c_0_40,plain,
multiply(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_41,plain,
multiply(X1,add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_42,plain,
add(X1,multiply(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_43,plain,
add(multiply(X1,X2),X2) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
add(X1,add(X2,X1)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_35]),c_0_30]) ).
cnf(c_0_45,plain,
multiply(add(X1,X2),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_46,plain,
multiply(X1,multiply(X2,X1)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_21]) ).
cnf(c_0_47,axiom,
add(multiply(X1,X2),add(multiply(X2,X3),multiply(X3,X1))) = multiply(add(X1,X2),multiply(add(X2,X3),add(X3,X1))),
distributivity ).
cnf(c_0_48,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_44]) ).
cnf(c_0_49,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_27]),c_0_46]) ).
cnf(c_0_50,plain,
add(multiply(X1,X2),multiply(inverse(X2),X1)) = multiply(add(X1,X2),add(inverse(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_15]),c_0_39]),c_0_13]),c_0_24]),c_0_48]),c_0_49]) ).
cnf(c_0_51,plain,
add(X1,add(n1,X2)) = n1,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_52,plain,
add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_53,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_54,plain,
multiply(X1,inverse(inverse(X1))) = add(X1,inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_15]),c_0_39]),c_0_13]),c_0_24]),c_0_49]),c_0_48]) ).
cnf(c_0_55,plain,
add(X1,add(inverse(X1),X2)) = add(n1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_56,plain,
add(n1,X1) = n1,
inference(spm,[status(thm)],[c_0_22,c_0_51]) ).
cnf(c_0_57,plain,
multiply(X1,multiply(add(X1,X2),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_58,plain,
multiply(add(X1,X2),add(multiply(X3,X1),X2)) = add(multiply(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_52]),c_0_49]) ).
cnf(c_0_59,plain,
add(multiply(X1,X2),multiply(inverse(X1),X2)) = multiply(add(X2,X1),add(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_60,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_35]) ).
cnf(c_0_61,plain,
add(X1,add(X2,X3)) = add(X2,add(X3,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_62,plain,
add(X1,add(inverse(X1),X2)) = n1,
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,plain,
multiply(X1,multiply(X2,add(X1,X3))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_46]),c_0_57]) ).
cnf(c_0_64,plain,
multiply(add(X1,X2),add(inverse(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_27]),c_0_57]),c_0_41]) ).
cnf(c_0_65,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_60]),c_0_49]),c_0_54]),c_0_60]) ).
cnf(c_0_66,plain,
add(X1,multiply(inverse(X1),add(X2,X1))) = add(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_41]),c_0_30]),c_0_31]),c_0_61]),c_0_62]),c_0_24]) ).
cnf(c_0_67,plain,
multiply(inverse(X1),add(X2,X1)) = multiply(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
add(multiply(X1,X2),multiply(X1,multiply(X2,X3))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_69,plain,
add(multiply(X1,X2),multiply(X2,inverse(X1))) = multiply(add(X1,X2),add(X2,inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_65]),c_0_48]),c_0_49]) ).
cnf(c_0_70,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_71,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_49]) ).
cnf(c_0_72,plain,
multiply(add(X1,X2),add(X1,add(X2,X3))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_73,plain,
add(X1,multiply(inverse(X1),X2)) = add(X2,X1),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,plain,
add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_44]),c_0_30]),c_0_44]) ).
cnf(c_0_75,plain,
add(multiply(X1,X2),add(multiply(X2,X1),X3)) = add(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_76,plain,
add(multiply(X1,X2),multiply(X2,X1)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_77,plain,
add(multiply(X1,X2),multiply(X2,X3)) = multiply(X2,add(multiply(X2,X3),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_53]),c_0_21]),c_0_42]),c_0_61]),c_0_68]),c_0_49]),c_0_41]),c_0_49]) ).
cnf(c_0_78,plain,
multiply(add(X1,X2),add(X2,inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_69]),c_0_42]),c_0_70]),c_0_35]) ).
cnf(c_0_79,plain,
add(X1,multiply(add(X1,X2),X3)) = multiply(add(X3,X1),add(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_35]),c_0_30]),c_0_36]),c_0_71]),c_0_72]),c_0_48]),c_0_27]),c_0_48]) ).
cnf(c_0_80,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_73,c_0_65]) ).
cnf(c_0_81,plain,
multiply(inverse(X1),multiply(add(X2,X1),X3)) = multiply(inverse(X1),multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_67]),c_0_21]) ).
cnf(c_0_82,plain,
add(multiply(X1,X2),X3) = add(X3,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_83,plain,
add(X1,multiply(X2,add(X3,X1))) = multiply(add(X3,X1),add(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_48]) ).
cnf(c_0_84,plain,
add(X1,multiply(X2,add(X1,X3))) = multiply(add(X2,X1),add(X1,X3)),
inference(spm,[status(thm)],[c_0_79,c_0_49]) ).
cnf(c_0_85,plain,
add(multiply(X1,X2),multiply(X2,inverse(X1))) = X2,
inference(rw,[status(thm)],[c_0_69,c_0_78]) ).
cnf(c_0_86,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(X2,add(multiply(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_77,c_0_49]) ).
cnf(c_0_87,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
prove_multiply_add_property ).
cnf(c_0_88,plain,
multiply(X1,multiply(X2,add(X3,multiply(X1,X2)))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_89,plain,
multiply(add(X1,X2),add(X2,X3)) = add(multiply(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_65]),c_0_73]),c_0_65]),c_0_82]),c_0_83]) ).
cnf(c_0_90,plain,
multiply(X1,add(multiply(X2,X1),X3)) = multiply(X1,add(X2,multiply(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),c_0_49]) ).
cnf(c_0_91,negated_conjecture,
add(multiply(a,b),multiply(a,c)) != multiply(a,add(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_49]),c_0_49]) ).
cnf(c_0_92,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(multiply(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_77,c_0_49]) ).
cnf(c_0_93,plain,
multiply(X1,add(X2,multiply(X3,X1))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_63]),c_0_90]) ).
cnf(c_0_94,negated_conjecture,
multiply(a,add(b,multiply(a,c))) != multiply(a,add(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_48]) ).
cnf(c_0_95,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(spm,[status(thm)],[c_0_93,c_0_49]) ).
cnf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.36 % Problem : BOO031-1 : TPTP v9.2.1. Released v2.2.0.
% 0.10/0.36 % 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
% 0.16/0.61 % Computer : n031.cluster.edu
% 0.16/0.61 % Model : x86_64 x86_64
% 0.16/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.61 % Memory : 8042.1875MB
% 0.16/0.61 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.61 % CPULimit : 300
% 0.16/0.61 % WCLimit : 300
% 0.16/0.61 % DateTime : Tue May 5 10:46:55 EDT 2026
% 0.16/0.61 % CPUTime :
% 0.19/0.63 % start to proof: theBenchmark
% 4.44/3.63 % Version : CSE_E---1.7
% 4.44/3.63 % Problem : theBenchmark.p
% 4.44/3.63 % SZS status Unsatisfiable for theBenchmark.p
% 4.44/3.63 % SZS output start CNFRefutation
% See solution above
% 4.44/3.64 % Total time : 2.369s
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