%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO022-1 : 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 : n020.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 04:11:10 PM UTC 2026
% Result : Unsatisfiable 2.18s 2.03s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 4 RR)
% Number of literals : 42 ( 41 equ; 3 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 : 81 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(add_multiply,axiom,
add(multiply(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply) ).
cnf(multiply_add,axiom,
multiply(add(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
cnf(add_multiply_property,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X2,X1),add(X3,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply_property) ).
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(multiplicative_inverse,axiom,
multiply(X1,inverse(X1)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse) ).
cnf(prove_associativity_of_multiply,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
cnf(c_0_7,axiom,
add(multiply(X1,X2),X2) = X2,
add_multiply ).
cnf(c_0_8,axiom,
multiply(add(X1,X2),X2) = X2,
multiply_add ).
cnf(c_0_9,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X2,X1),add(X3,X1)),
add_multiply_property ).
cnf(c_0_10,plain,
add(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
multiply_add_property ).
cnf(c_0_12,plain,
add(X1,multiply(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8]) ).
cnf(c_0_13,plain,
multiply(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_14,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_10]) ).
cnf(c_0_15,plain,
multiply(X1,add(X2,multiply(X3,X1))) = add(multiply(X3,X1),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_16,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_9]),c_0_13]) ).
cnf(c_0_18,plain,
add(multiply(X1,X2),multiply(X2,X3)) = multiply(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_14]),c_0_15]),c_0_11]) ).
cnf(c_0_19,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
add(X1,inverse(X1)) = n1,
additive_inverse ).
cnf(c_0_21,axiom,
multiply(X1,inverse(X1)) = n0,
multiplicative_inverse ).
cnf(c_0_22,plain,
multiply(X1,add(X2,multiply(X3,X1))) = multiply(X1,add(X3,X2)),
inference(rw,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_23,plain,
add(X1,n0) = multiply(X1,n1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_24,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_13]),c_0_17]),c_0_12]),c_0_16]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(X2,add(X3,X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_12]) ).
cnf(c_0_26,plain,
add(n0,X1) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_27,plain,
multiply(X1,n1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_23]) ).
cnf(c_0_28,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_29,plain,
add(n0,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(X2,X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_31,plain,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,X2),multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_28,c_0_12]) ).
cnf(c_0_33,plain,
multiply(inverse(X1),add(X1,X2)) = multiply(inverse(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_29]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_32]) ).
cnf(c_0_35,plain,
multiply(inverse(X1),multiply(X1,X2)) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_24]),c_0_14]),c_0_21]) ).
cnf(c_0_36,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
prove_associativity_of_multiply ).
cnf(c_0_38,plain,
multiply(X1,multiply(X2,add(inverse(X1),X3))) = multiply(X3,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_35]),c_0_29]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
multiply(c,multiply(a,b)) != multiply(a,multiply(b,c)),
inference(rw,[status(thm)],[c_0_37,c_0_14]) ).
cnf(c_0_40,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_35]),c_0_29]),c_0_36]),c_0_38]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_14]),c_0_40]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO022-1 : 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
% 0.14/0.32 % Computer : n020.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 10:46:35 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 2.18/2.03 % Version : CSE_E---1.7
% 2.18/2.03 % Problem : theBenchmark.p
% 2.18/2.03 % SZS status Unsatisfiable for theBenchmark.p
% 2.18/2.03 % SZS output start CNFRefutation
% See solution above
% 2.18/2.03 % Total time : 1.370s
%------------------------------------------------------------------------------