%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN079-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n021.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 : Fri Sep  1 03:33:04 EDT 2023

% Result   : Unsatisfiable 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYN079-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 20:54:42 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.40  Command-line arguments: --no-flatten-goal
% 0.21/0.40  
% 0.21/0.40  % SZS status Unsatisfiable
% 0.21/0.40  
% 0.21/0.40  % SZS output start Proof
% 0.21/0.40  Take the following subset of the input axioms:
% 0.21/0.40    fof(clause_1, axiom, big_f(f(a, b), f(b, c))).
% 0.21/0.40    fof(clause_2, axiom, big_f(f(b, c), f(a, c))).
% 0.21/0.40    fof(clause_3, axiom, ![X, Y, Z]: (~big_f(X, Y) | (~big_f(Y, Z) | big_f(X, Z)))).
% 0.21/0.40    fof(prove_this, negated_conjecture, ~big_f(f(a, b), f(a, c))).
% 0.21/0.40  
% 0.21/0.40  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.40  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.40  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.40    fresh(y, y, x1...xn) = u
% 0.21/0.40    C => fresh(s, t, x1...xn) = v
% 0.21/0.40  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.40  variables of u and v.
% 0.21/0.40  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.40  input problem has no model of domain size 1).
% 0.21/0.40  
% 0.21/0.40  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.40  
% 0.21/0.40  Axiom 1 (clause_3): fresh2(X, X, Y, Z) = true.
% 0.21/0.40  Axiom 2 (clause_3): fresh(X, X, Y, Z, W) = big_f(Y, W).
% 0.21/0.40  Axiom 3 (clause_1): big_f(f(a, b), f(b, c)) = true.
% 0.21/0.40  Axiom 4 (clause_2): big_f(f(b, c), f(a, c)) = true.
% 0.21/0.40  Axiom 5 (clause_3): fresh(big_f(X, Y), true, Z, X, Y) = fresh2(big_f(Z, X), true, Z, Y).
% 0.21/0.40  
% 0.21/0.40  Goal 1 (prove_this): big_f(f(a, b), f(a, c)) = true.
% 0.21/0.40  Proof:
% 0.21/0.40    big_f(f(a, b), f(a, c))
% 0.21/0.40  = { by axiom 2 (clause_3) R->L }
% 0.21/0.40    fresh(true, true, f(a, b), f(b, c), f(a, c))
% 0.21/0.40  = { by axiom 4 (clause_2) R->L }
% 0.21/0.40    fresh(big_f(f(b, c), f(a, c)), true, f(a, b), f(b, c), f(a, c))
% 0.21/0.40  = { by axiom 5 (clause_3) }
% 0.21/0.40    fresh2(big_f(f(a, b), f(b, c)), true, f(a, b), f(a, c))
% 0.21/0.40  = { by axiom 3 (clause_1) }
% 0.21/0.40    fresh2(true, true, f(a, b), f(a, c))
% 0.21/0.40  = { by axiom 1 (clause_3) }
% 0.21/0.40    true
% 0.21/0.40  % SZS output end Proof
% 0.21/0.40  
% 0.21/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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