%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP665-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n029.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 : Thu Aug 31 01:15:56 EDT 2023

% Result   : Unsatisfiable 0.48s 0.75s
% Output   : CNFRefutation 0.48s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP665-10 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13  % Command    : toma --casc %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 22:00:41 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.48/0.75  % SZS status Unsatisfiable
% 0.48/0.75  % SZS output start Proof
% 0.48/0.75  original problem:
% 0.48/0.75  axioms:
% 0.48/0.75  mult(A, ld(A, B)) = B
% 0.48/0.75  ld(A, mult(A, B)) = B
% 0.48/0.75  mult(rd(A, B), B) = A
% 0.48/0.75  rd(mult(A, B), B) = A
% 0.48/0.75  mult(A, unit()) = A
% 0.48/0.75  mult(unit(), A) = A
% 0.48/0.75  mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C))
% 0.48/0.75  mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))
% 0.48/0.75  mult(op_c(), A) = mult(A, op_c())
% 0.48/0.75  goal:
% 0.48/0.75  mult(op_c(), mult(x0(), x1())) != mult(mult(op_c(), x0()), x1())
% 0.48/0.75  To show the unsatisfiability of the original goal,
% 0.48/0.75  it suffices to show that mult(op_c(), mult(x0(), x1())) = mult(mult(op_c(), x0()), x1()) (skolemized goal) is valid under the axioms.
% 0.48/0.75  Here is an equational proof:
% 0.48/0.75  1: ld(X0, mult(X0, X1)) = X1.
% 0.48/0.75  Proof: Axiom.
% 0.48/0.75  
% 0.48/0.75  7: mult(mult(X0, X1), X2) = mult(mult(X0, X2), ld(X2, mult(X1, X2))).
% 0.48/0.75  Proof: Axiom.
% 0.48/0.75  
% 0.48/0.75  8: mult(op_c(), X0) = mult(X0, op_c()).
% 0.48/0.75  Proof: Axiom.
% 0.48/0.75  
% 0.48/0.75  14: op_c() = ld(X2, mult(op_c(), X2)).
% 0.48/0.75  Proof: A critical pair between equations 1 and 8.
% 0.48/0.75  
% 0.48/0.75  31: mult(mult(X3, X2), ld(X2, mult(op_c(), X2))) = mult(mult(op_c(), X3), X2).
% 0.48/0.75  Proof: A critical pair between equations 7 and 8.
% 0.48/0.75  
% 0.48/0.75  35: mult(op_c(), mult(X3, X2)) = mult(mult(op_c(), X3), X2).
% 0.48/0.75  Proof: Rewrite equation 31,
% 0.48/0.75                 lhs with equations [14,8]
% 0.48/0.75                 rhs with equations [].
% 0.48/0.75  
% 0.48/0.75  36: mult(op_c(), mult(x0(), x1())) = mult(mult(op_c(), x0()), x1()).
% 0.48/0.75  Proof: Rewrite lhs with equations []
% 0.48/0.75                 rhs with equations [35].
% 0.48/0.75  
% 0.48/0.75  % SZS output end Proof
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