%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO025-1 : 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 : n025.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 3.59s 3.12s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 19 RR)
% Number of literals : 84 ( 83 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 : 126 ( 24 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_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(additive_inverse,axiom,
add(X1,inverse(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
cnf(multiply_add,axiom,
multiply(add(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
cnf(pixley2,axiom,
pixley(X1,X2,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley2) ).
cnf(pixley3,axiom,
pixley(X1,X2,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley3) ).
cnf(prove_equal_identity,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_identity) ).
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,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_11,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
multiply_add_property ).
cnf(c_0_12,axiom,
add(X1,inverse(X1)) = n1,
additive_inverse ).
cnf(c_0_13,plain,
add(multiply(X1,inverse(X1)),multiply(X2,n1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_14,axiom,
multiply(add(X1,X2),X2) = X2,
multiply_add ).
cnf(c_0_15,axiom,
pixley(X1,X2,X2) = X1,
pixley2 ).
cnf(c_0_16,plain,
add(multiply(X1,inverse(X1)),n1) = add(X2,n1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
multiply(n1,inverse(X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_18,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X2),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,add(X2,X3)),multiply(X3,X1)) = multiply(X3,X1),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_20,axiom,
pixley(X1,X2,X1) = X1,
pixley3 ).
cnf(c_0_21,plain,
add(inverse(n1),n1) = add(X1,n1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
add(multiply(X1,inverse(X2)),multiply(X2,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_23,plain,
multiply(multiply(X1,multiply(X2,add(X3,X4))),multiply(multiply(X4,X2),X1)) = multiply(multiply(X4,X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_24,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X1),multiply(inverse(X2),X1))) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_9]) ).
cnf(c_0_25,plain,
multiply(X1,add(add(X2,X1),X3)) = add(X1,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_26,plain,
add(X1,n1) = add(X2,n1),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_27,plain,
multiply(X1,multiply(X2,add(X1,inverse(X2)))) = multiply(X2,add(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_28,plain,
multiply(multiply(X1,multiply(X2,n1)),multiply(multiply(inverse(X3),X2),X1)) = multiply(multiply(inverse(X3),X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_29,plain,
multiply(multiply(inverse(X1),add(X2,n1)),inverse(X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_30,plain,
add(multiply(X1,inverse(X2)),multiply(X1,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_31,plain,
add(inverse(X1),multiply(X2,inverse(X1))) = multiply(inverse(X1),add(n1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,n1),multiply(inverse(X2),X1)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_33,plain,
multiply(X1,add(X2,n1)) = add(X1,multiply(n1,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(X1,n1)) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_35,plain,
multiply(multiply(X1,add(X2,inverse(X1))),multiply(multiply(inverse(X1),X1),X2)) = multiply(multiply(inverse(X1),X1),X2),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_36,plain,
multiply(multiply(inverse(X1),n1),inverse(X1)) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_14]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,X2),add(X3,multiply(X2,add(X4,X1)))) = add(multiply(X3,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_38,plain,
add(inverse(X1),multiply(n1,add(n1,inverse(X1)))) = n1,
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_39,plain,
add(inverse(X1),inverse(X1)) = multiply(inverse(X1),add(n1,n1)),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_40,plain,
multiply(n1,multiply(inverse(X1),add(X2,n1))) = multiply(inverse(X1),add(X2,n1)),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_41,plain,
multiply(multiply(n1,n1),add(X1,n1)) = multiply(n1,add(n1,n1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_11]) ).
cnf(c_0_42,plain,
multiply(multiply(n1,add(inverse(n1),inverse(n1))),inverse(n1)) = inverse(n1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
add(multiply(X1,multiply(inverse(X2),X3)),multiply(inverse(X2),X3)) = multiply(multiply(inverse(X2),X3),add(X1,multiply(X3,n1))),
inference(spm,[status(thm)],[c_0_11,c_0_32]) ).
cnf(c_0_44,plain,
multiply(inverse(X1),add(n1,n1)) = multiply(multiply(inverse(X1),n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]),c_0_11]),c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
multiply(multiply(add(X1,n1),add(X2,multiply(n1,n1))),multiply(n1,add(n1,n1))) = multiply(n1,add(n1,n1)),
inference(spm,[status(thm)],[c_0_19,c_0_41]) ).
cnf(c_0_46,plain,
add(inverse(n1),multiply(X1,n1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_47,plain,
multiply(multiply(n1,multiply(inverse(n1),add(n1,n1))),inverse(n1)) = inverse(n1),
inference(rw,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_48,plain,
multiply(multiply(inverse(X1),X1),add(multiply(X2,inverse(X1)),multiply(X1,n1))) = multiply(multiply(inverse(X1),X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_43]) ).
cnf(c_0_49,plain,
multiply(inverse(X1),add(X2,n1)) = multiply(multiply(inverse(X1),n1),n1),
inference(spm,[status(thm)],[c_0_44,c_0_26]) ).
cnf(c_0_50,plain,
multiply(n1,multiply(n1,add(n1,n1))) = multiply(n1,add(n1,n1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_14]) ).
cnf(c_0_51,plain,
multiply(inverse(n1),add(n1,multiply(n1,multiply(inverse(n1),add(n1,n1))))) = multiply(inverse(n1),add(n1,n1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_47]),c_0_39]) ).
cnf(c_0_52,plain,
multiply(multiply(X1,multiply(multiply(inverse(X2),X2),X3)),multiply(multiply(inverse(X2),X2),X1)) = multiply(multiply(inverse(X2),X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_48]),c_0_32]),c_0_32]) ).
cnf(c_0_53,plain,
multiply(n1,multiply(multiply(inverse(X1),n1),n1)) = multiply(multiply(inverse(X1),n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_49]),c_0_49]) ).
cnf(c_0_54,plain,
multiply(multiply(X1,X2),multiply(multiply(X2,n1),X1)) = multiply(multiply(X2,n1),X1),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_55,plain,
multiply(n1,multiply(n1,add(X1,n1))) = multiply(n1,add(X1,n1)),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_56,plain,
multiply(inverse(n1),add(n1,multiply(inverse(n1),add(n1,n1)))) = multiply(inverse(n1),add(n1,n1)),
inference(rw,[status(thm)],[c_0_51,c_0_40]) ).
cnf(c_0_57,plain,
add(multiply(X1,n1),multiply(X2,multiply(X1,n1))) = multiply(multiply(X1,n1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_58,plain,
multiply(multiply(multiply(inverse(n1),n1),n1),multiply(multiply(inverse(n1),n1),n1)) = multiply(multiply(inverse(n1),n1),n1),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
multiply(multiply(multiply(inverse(X1),n1),n1),inverse(X1)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_44]),c_0_14]),c_0_17]),c_0_14]),c_0_17]) ).
cnf(c_0_60,plain,
multiply(n1,add(n1,multiply(n1,n1))) = add(n1,multiply(n1,n1)),
inference(spm,[status(thm)],[c_0_55,c_0_25]) ).
cnf(c_0_61,plain,
multiply(X1,add(X2,add(X3,X1))) = add(multiply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_62,plain,
multiply(inverse(n1),add(n1,multiply(multiply(inverse(n1),n1),n1))) = multiply(multiply(inverse(n1),n1),n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_44]),c_0_44]) ).
cnf(c_0_63,plain,
multiply(multiply(inverse(n1),n1),n1) = inverse(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_11]),c_0_11]),c_0_39]),c_0_44]),c_0_53]),c_0_53]),c_0_11]),c_0_46]),c_0_17]),c_0_59]) ).
cnf(c_0_64,plain,
multiply(add(n1,multiply(n1,n1)),multiply(multiply(n1,n1),n1)) = multiply(multiply(n1,n1),n1),
inference(spm,[status(thm)],[c_0_19,c_0_60]) ).
cnf(c_0_65,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_19,c_0_14]),c_0_61]),c_0_61]) ).
cnf(c_0_66,plain,
multiply(inverse(n1),n1) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63]),c_0_12]),c_0_63]) ).
cnf(c_0_67,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_61]) ).
cnf(c_0_68,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_57,c_0_64]),c_0_11]),c_0_11]),c_0_55]) ).
cnf(c_0_69,plain,
add(multiply(X1,multiply(X2,n1)),multiply(X2,n1)) = multiply(multiply(X2,n1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_61,c_0_13]) ).
cnf(c_0_70,plain,
multiply(add(X1,n1),add(X2,n1)) = add(X2,n1),
inference(spm,[status(thm)],[c_0_65,c_0_26]) ).
cnf(c_0_71,plain,
multiply(n1,add(inverse(n1),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_66]),c_0_46]) ).
cnf(c_0_72,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_67,c_0_68]),c_0_69]),c_0_41]),c_0_11]),c_0_70]),c_0_11]),c_0_60]),c_0_14]) ).
cnf(c_0_73,plain,
add(n1,n1) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_71]),c_0_72]) ).
cnf(c_0_74,plain,
multiply(n1,n1) = n1,
inference(spm,[status(thm)],[c_0_14,c_0_73]) ).
cnf(c_0_75,plain,
multiply(inverse(n1),X1) = inverse(n1),
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_48,c_0_74]),c_0_66]),c_0_49]),c_0_66]),c_0_66]),c_0_66]) ).
cnf(c_0_76,plain,
multiply(n1,X1) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_71,c_0_46]) ).
cnf(c_0_77,plain,
inverse(inverse(n1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_12]),c_0_74]) ).
cnf(c_0_78,plain,
add(inverse(X1),inverse(n1)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_75]),c_0_12]),c_0_76]),c_0_17]) ).
cnf(c_0_79,plain,
multiply(X1,inverse(n1)) = inverse(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_77]),c_0_49]),c_0_76]),c_0_17]),c_0_76]),c_0_17]),c_0_49]),c_0_76]),c_0_17]),c_0_76]),c_0_17]) ).
cnf(c_0_80,plain,
add(inverse(n1),inverse(X1)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_78]),c_0_79]),c_0_17]) ).
cnf(c_0_81,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
prove_equal_identity ).
cnf(c_0_82,plain,
multiply(X1,inverse(X1)) = inverse(n1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_80]),c_0_75]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO025-1 : 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
% 0.16/0.33 % Computer : n025.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 : Tue May 5 10:45:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.59/3.12 % Version : CSE_E---1.7
% 3.59/3.12 % Problem : theBenchmark.p
% 3.59/3.12 % SZS status Unsatisfiable for theBenchmark.p
% 3.59/3.12 % SZS output start CNFRefutation
% See solution above
% 3.70/3.13 % Total time : 2.369s
%------------------------------------------------------------------------------