%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO024-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n004.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 04:11:20 PM UTC 2026
% Result : Unsatisfiable 1.99s 1.93s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of clauses : 82 ( 82 unt; 0 nHn; 21 RR)
% Number of literals : 82 ( 81 equ; 2 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 125 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(pixley1,axiom,
pixley(X1,X1,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley1) ).
cnf(pixley_defn,axiom,
pixley(X1,X2,X3) = add(multiply(X1,inverse(X2)),add(multiply(X1,X3),multiply(inverse(X2),X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley_defn) ).
cnf(multiply_add,axiom,
multiply(add(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
cnf(multiply_add_property,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(pixley3,axiom,
pixley(X1,X2,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley3) ).
cnf(additive_inverse,axiom,
add(X1,inverse(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
cnf(pixley2,axiom,
pixley(X1,X2,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley2) ).
cnf(prove_add_multiply,negated_conjecture,
add(multiply(a,b),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_add_multiply) ).
cnf(c_0_8,axiom,
pixley(X1,X1,X2) = X2,
pixley1 ).
cnf(c_0_9,axiom,
pixley(X1,X2,X3) = add(multiply(X1,inverse(X2)),add(multiply(X1,X3),multiply(inverse(X2),X3))),
pixley_defn ).
cnf(c_0_10,axiom,
multiply(add(X1,X2),X2) = X2,
multiply_add ).
cnf(c_0_11,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
multiply_add_property ).
cnf(c_0_12,axiom,
pixley(X1,X2,X1) = X1,
pixley3 ).
cnf(c_0_13,plain,
add(multiply(X1,inverse(X1)),add(multiply(X1,X2),multiply(inverse(X1),X2))) = X2,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,axiom,
add(X1,inverse(X1)) = n1,
additive_inverse ).
cnf(c_0_15,plain,
multiply(multiply(X1,add(X2,X3)),multiply(X3,X1)) = multiply(X3,X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
multiply(X1,add(X2,add(X3,X1))) = add(multiply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_17,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X1),multiply(inverse(X2),X1))) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_18,plain,
add(multiply(X1,inverse(X1)),multiply(X2,n1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_14]) ).
cnf(c_0_19,plain,
multiply(add(X1,X2),add(multiply(X3,X2),X2)) = add(multiply(X3,X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
add(multiply(X1,inverse(X2)),multiply(X1,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_21,plain,
multiply(n1,inverse(X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_22,axiom,
pixley(X1,X2,X2) = X1,
pixley2 ).
cnf(c_0_23,plain,
add(multiply(X1,inverse(X1)),n1) = add(X2,n1),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_24,plain,
multiply(add(X1,X2),add(X2,X2)) = add(X2,X2),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_25,plain,
add(inverse(X1),multiply(n1,add(n1,inverse(X1)))) = n1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X2),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_27,plain,
multiply(X1,add(add(X2,X1),X3)) = add(X1,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_28,plain,
add(X1,n1) = add(X2,n1),
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_29,plain,
add(add(multiply(X1,X2),X2),multiply(X3,add(X1,add(X4,X2)))) = multiply(add(X1,add(X4,X2)),add(X2,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_30,plain,
multiply(add(X1,multiply(X2,X3)),multiply(X3,add(X2,X2))) = multiply(X3,add(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_11]),c_0_11]) ).
cnf(c_0_31,plain,
multiply(n1,multiply(add(n1,inverse(X1)),add(n1,n1))) = multiply(add(n1,inverse(X1)),add(n1,n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11]),c_0_11]) ).
cnf(c_0_32,plain,
add(multiply(X1,inverse(X2)),multiply(X2,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_11]) ).
cnf(c_0_33,plain,
multiply(n1,add(inverse(X1),inverse(X1))) = add(inverse(X1),inverse(X1)),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_34,plain,
multiply(X1,add(X2,n1)) = add(X1,multiply(n1,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
add(X1,multiply(multiply(X2,add(X3,add(X4,X1))),X1)) = multiply(X1,multiply(add(X3,add(X4,X1)),add(X1,X2))),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_36,plain,
multiply(add(X1,add(multiply(X2,X3),X3)),add(X3,X3)) = add(X3,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_10]),c_0_16]) ).
cnf(c_0_37,plain,
add(multiply(X1,add(X2,add(X3,X4))),add(multiply(X2,X4),X4)) = multiply(add(X2,add(X3,X4)),add(X1,X4)),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_38,plain,
multiply(n1,multiply(n1,add(n1,n1))) = multiply(n1,add(n1,n1)),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_39,plain,
add(multiply(inverse(n1),inverse(n1)),add(inverse(n1),inverse(n1))) = inverse(n1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
add(multiply(X1,inverse(X2)),inverse(X2)) = multiply(inverse(X2),add(X1,n1)),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_41,plain,
multiply(inverse(X1),add(X2,n1)) = add(inverse(X1),inverse(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_42,plain,
multiply(X1,multiply(add(X2,add(X3,X1)),add(X1,X1))) = add(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_16]),c_0_10]) ).
cnf(c_0_43,plain,
multiply(multiply(add(X1,add(X2,X3)),add(X4,X3)),add(X3,X3)) = add(X3,X3),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
multiply(n1,multiply(n1,add(X1,n1))) = multiply(n1,add(X1,n1)),
inference(spm,[status(thm)],[c_0_38,c_0_28]) ).
cnf(c_0_45,plain,
add(inverse(n1),inverse(n1)) = multiply(inverse(n1),inverse(n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_39]),c_0_40]),c_0_41]) ).
cnf(c_0_46,plain,
multiply(X1,add(X1,X1)) = add(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_43]) ).
cnf(c_0_47,plain,
multiply(n1,add(n1,multiply(n1,n1))) = add(n1,multiply(n1,n1)),
inference(spm,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_48,plain,
add(inverse(X1),multiply(X2,inverse(X1))) = multiply(inverse(X1),add(n1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_49,plain,
multiply(inverse(n1),inverse(n1)) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_45]),c_0_11]),c_0_46]),c_0_45]) ).
cnf(c_0_50,plain,
add(multiply(X1,n1),multiply(X2,multiply(X1,n1))) = multiply(multiply(X1,n1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_51,plain,
multiply(add(n1,multiply(n1,n1)),multiply(multiply(n1,n1),n1)) = multiply(multiply(n1,n1),n1),
inference(spm,[status(thm)],[c_0_15,c_0_47]) ).
cnf(c_0_52,plain,
multiply(X1,multiply(X1,n1)) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_53,plain,
multiply(multiply(X1,n1),multiply(inverse(X2),X1)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_54,plain,
multiply(inverse(n1),n1) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_45]),c_0_49]),c_0_14]) ).
cnf(c_0_55,plain,
multiply(multiply(multiply(n1,n1),n1),add(multiply(n1,n1),add(n1,multiply(n1,n1)))) = multiply(n1,add(n1,n1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_11]),c_0_11]),c_0_44]) ).
cnf(c_0_56,plain,
add(multiply(X1,multiply(X2,n1)),multiply(X2,n1)) = multiply(multiply(X2,n1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_57,plain,
multiply(multiply(n1,n1),add(X1,n1)) = multiply(n1,add(n1,n1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_52]),c_0_11]) ).
cnf(c_0_58,plain,
multiply(multiply(n1,n1),inverse(n1)) = inverse(n1),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
add(n1,multiply(n1,n1)) = add(n1,n1),
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_29,c_0_55]),c_0_56]),c_0_57]),c_0_11]),c_0_24]),c_0_11]),c_0_47]),c_0_10]) ).
cnf(c_0_60,plain,
add(add(X1,X1),multiply(X2,add(X1,X1))) = multiply(add(X1,X1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_46]) ).
cnf(c_0_61,plain,
multiply(inverse(n1),add(n1,n1)) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_58]),c_0_45]),c_0_49]),c_0_59]) ).
cnf(c_0_62,plain,
add(add(n1,n1),inverse(n1)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_14]),c_0_10]) ).
cnf(c_0_63,plain,
add(X1,multiply(inverse(add(X2,X1)),X1)) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_64,plain,
add(inverse(n1),inverse(n1)) = inverse(n1),
inference(rw,[status(thm)],[c_0_45,c_0_49]) ).
cnf(c_0_65,plain,
add(inverse(n1),multiply(X1,n1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_66,plain,
multiply(n1,n1) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_62]),c_0_54]),c_0_14]) ).
cnf(c_0_67,plain,
multiply(inverse(n1),add(n1,inverse(inverse(n1)))) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_48]),c_0_54]) ).
cnf(c_0_68,plain,
add(inverse(n1),n1) = n1,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
add(add(X1,X1),add(X1,X1)) = add(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_46]),c_0_24]) ).
cnf(c_0_70,plain,
add(inverse(inverse(n1)),inverse(n1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_67]),c_0_21]) ).
cnf(c_0_71,plain,
add(X1,n1) = n1,
inference(spm,[status(thm)],[c_0_28,c_0_68]) ).
cnf(c_0_72,plain,
multiply(add(X1,X1),add(X2,X2)) = multiply(X2,add(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_11]),c_0_11]) ).
cnf(c_0_73,plain,
inverse(inverse(n1)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_70]),c_0_66]),c_0_71]) ).
cnf(c_0_74,plain,
multiply(X1,add(X2,X2)) = multiply(X2,add(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_69]),c_0_72]),c_0_72]) ).
cnf(c_0_75,plain,
multiply(n1,add(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_73]),c_0_71]),c_0_11]) ).
cnf(c_0_76,plain,
multiply(X1,n1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_71]) ).
cnf(c_0_77,plain,
multiply(n1,add(X1,X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_76]),c_0_76]) ).
cnf(c_0_78,plain,
multiply(n1,X1) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_32]) ).
cnf(c_0_79,negated_conjecture,
add(multiply(a,b),b) != b,
prove_add_multiply ).
cnf(c_0_80,plain,
add(multiply(X1,X2),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_78]),c_0_71]),c_0_76]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO024-1 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.17/0.33 % Computer : n004.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 10:45:02 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.99/1.93 % Version : CSE_E---1.7
% 1.99/1.93 % Problem : theBenchmark.p
% 1.99/1.93 % SZS status Unsatisfiable for theBenchmark.p
% 1.99/1.93 % SZS output start CNFRefutation
% See solution above
% 1.99/1.93 % Total time : 1.375s
%------------------------------------------------------------------------------